Hendrick joined Derby County as a youth player in 2008 from St Kevin’s Boys in Dublin, having overcome Osgood-Schlatter disease, and played regularly for the club’s academy side before breaking into the reserve team during the 2009–10 campaign. He made one start and seven substitute appearances as the club’s reserve side successfully captured the 2009–10 Central League Central Section title. At the end of the season his first involvement with the Derby County first team came on 2 May 2010 as he was an unused substitute in a 2–0 victory over Cardiff City in the final match of the 2009–10 season. A few weeks later, on 8 July 2010, he signed his first professional contract, alongside four other Derby County academy graduates, including fellow Republic of Ireland Youth international Ryan Connolly and future League of Ireland player Graham Kelly.

Born in Dublin, Hendrick has been capped by Ireland at under-15, under-16, under-17, under-18, under-19 and under-21 levels. He was shortlisted for the Republic of Ireland under-17 level International Player of the Year award in July 2010. He played a key role in the U19s successful 2011 European Under-19 Championship qualifying campaign putting in a “string of impressive displays” as he featured in all three group matches and notched the only goal of the match in a 1–0 win over Poland U19s. In July 2011, Hendrick was named in the squad for the European Under-19 Championships. He started in all four of Ireland’s matches at the tournament as they were knocked out in the semi-final stage to Spain.

Hendrick played a more significant role in Derby’s reserve side during the 2010–11 season, making 17 starts in all competitions and scoring 9 goals, including a hat-trick in a 14–1 victory over Shirebrook Town in the Derbyshire Senior Cup and a brace in a 5–0 win over Buxton in the final of the same competition. Throughout the campaign, Hendrick impressed enough to earn a contract extension at Derby, which he signed in January 2011 to take him through until Summer 2012.

Approaching the end of the 2010–11 campaign, Derby manager Nigel Clough stated his desire to give Hendrick a run in the first team, stating “(He’s) progressed and done well this season…we would love to see him in the team for three or four games.” He made his debut in the following match on 23 April 2011, as an 80th-minute replacement for Robbie Savage in a 4–2 home defeat to Burnley.

Upon his return from the tournament, Hendrick was called up to the Irish U21 squad for the first time. He made his debut in a 2–1 victory against Austria U21s on 9 August 2011.

Hendrick missed Derby’s Christmas and New Year programme of fixtures with an ankle ligament injury in a 1–0 defeat against Ipswich Town. He returned to the first team squad as an unused substitute in a 1–0 win against Coventry City on 14 January 2012, returning to playing action a week later in the 0–0 draw at Burnley as a 47th-minute substitute. Hendrick became a mainstay of the Derby team for the remainder of the season after this fixture, displacing James Bailey in central midfield. He scored his third goal of the season in a 3–2 home win against Crystal Palace on 24 March. Hendrick’s form throughout the season was rewarded when he won the club’s Sammy Crooks Young Player of the Year award.

Hendrick began the 2012–13 season in the starting eleven but after poor performances and scoring only once in his first 16 matches, he was dropped for Michael Jacobs in the 3–2 victory over Birmingham City on 24 November 2012. He regained his starting place shortly afterwards, and admitted he was struggling to replicate his previous season’s performances. Hendrick’s form soon improved and he scored his second goal of the season in a 2–0 win at Bristol City on 15 December.

Hendrick started 2013 in good form, scoring three goals in the opening three matches, including a goal against Middlesbrough in a 3–1 home win which was later named Derby’s Goal of the Season. Former Derby teammate Kevin Kilbane stated that Hendrick had the ability to play in the Premier League. He scored again on 9 February 2013, in a 2–2 draw against Sheffield Wednesday. He earned further praise for his performance in Derby’s 3–0 win at home to Bristol City on 29 March, where he scored the opening goal.

In January 2013, it was reported that Ireland head coach Giovanni Trappatoni was watching Hendrick with the view to giving the player his first call-up to the senior side and later in the month Hendrick was called up to the senior squad to play in a friendly against Poland on 6 February 2013. Hendrick came on as a 71st-minute substitute for James McCarthy in the 2–0 win and provided an assist for Wes Hoolahan for Ireland’s second goal in this match, showing great composure in doing so with a well-executed pass. Hendrick received his first Ireland start in his fourth cap, in a match against World and European Champions Spain on 12 June 2013 at the Yankee Stadium in New York City. He played a starring role in the Euro 2016 qualifier against Georgia in the Aviva Stadium on 7 September 2015. His run and nutmeg set up an easy finish for Jonathan Walters which proved to be the only goal of the match.

Hendrick scored four league goals during the 2013–14 season, helping Derby reach the play-offs. In the play-off semi-final, Derby came up against Brighton & Hove Albion. On 11 May 2014, Hendrick scored in the 4–1 home victory in the second leg as Brighton were defeated 6–2 on aggregate. On 24 May, he played in the play-off final as Derby lost 1–0 to Queens Park Rangers thereby missing out on promotion to the Premier League.

On 26 June 2014, Hendrick agreed a new four-year contract with Derby, which would keep him at the club until the end of the 2017–18 season.

Hendrick scored his first goal of the 2014–15 season in the league opener against Rotherham United on 9 August 2014 which ended in a 1–0 win for Derby. He scored his fourth and fifth goals of the season on 8 November in a 5–0 thrashing of Wolverhampton Wanderers as Derby moved to the top of the Championship. Hendrick’s 85th-minute equaliser in the 3–3 draw at Millwall on 25 April 2015 helped keep alive the team’s play-off hopes. Derby needed a victory in their final match against Reading to secure a play-off place but lost 3–0 and finished the 2014–15 season in eighth position as ultimately they had earned just 12 points out of a possible 39 since beating Charlton Athletic in February. This season was Hendrick’s most fruitful to date in terms of goalscoring as he netted a total of nine goals in 47 matches in all competitions.

Hendrick scored his first goal of the 2015–16 season in a 2–2 draw away at Leeds United on 29 December 2015. He scored his second of the season in the 3–1 away win against Brentford on 20 February 2016. After being out of first-team action since March, Hendrick returned for the final league match against Ipswich Town on 7 May but was an unused substitute. Derby finished in fifth place in the Championship and qualified for the play-offs where they would meet Hull City in the semi-final. Hendrick was again an unused substitute in the semi-final first leg but returned to the starting line-up for the second leg and played the full 90 minutes as Derby lost 3–2 on aggregate to the Tigers.

Hendrick’s 2016–17 season did not get off to a good start as he picked up a hamstring injury in a 2–0 loss to Barnsley on 13 August 2016.

On 31 August 2016, Hendrick joined Premier League side Burnley for a club record £10.5 million fee on a three-year deal. He made his debut on 10 September, coming on as a 75th-minute substitute in a 1–1 draw at home to Hull City. He made his first start for Burnley on 17 September, playing the full 90 minutes in a 3–0 away defeat against reigning Premier League champions Leicester City. Nine days later, Hendrick netted his first goal for Burnley in a 2–0 home win over Watford with a header from a Steven Defour cross.

He scored his second goal for his new club on 10 December 2016 with a 25-yard volley in a 3–2 home victory over Bournemouth. Hendrick’s strike was nominated for Goal of the Month; it came third in the public vote, behind strikes by Alexis Sánchez in second and Henrikh Mkhitaryan in first and would later earn him the Burnley Goal of the Season award. On 4 February 2017, he was sent off against Watford in the sixth minute for a two-footed challenge on José Holebas as Burnley were defeated 2–1 at Vicarage Road.

Hendrick scored his first goal for Ireland on 5 September 2016. He opened the scoring in the third minute in the 2–2 away draw against Serbia in a 2018 World Cup qualifying match with a low shot just outside the penalty area which was deflected in off Branislav Ivanović.

On 20 June 2018, it was announced that Burnley would face Scottish Premiership club Aberdeen in the second qualifying round of the Europa League. Hendrick made his Europa League debut when he started on 26 July 2018 at Pittodrie Stadium. He was replaced by Sam Vokes in the 67th minute with Vokes eventually going on to score the equaliser to make it 1–1 in the 80th minute. The match ended 1–1, meaning Burnley had the advantage of an away goal. Burnley were eventually eliminated in the play-off round with a 4–2 aggregate defeat to Olympiacos. Hendrick played in all six matches of The Clarets’ Europa League campaign.

His first goal of the 2018–19 season came on 26 August 2018 in a 4–2 away defeat against newly promoted Fulham. Hendrick signed a one-year contract extension on 20 December 2018 with manager Sean Dyche stating his praise for the midfielder: “He’s done well for us. We have asked a lot of him. We have used him in a number of different positions that sometimes aren’t natural to him and over time he has delivered good performances for us.”

On 22 April 2019, Hendrick opened the scoring in a 2–2 draw against Chelsea at Stamford Bridge with a fine volley for his third goal of the season. This draw saw Burnley reach 40 points, virtually guaranteeing their safety in the Premier League. Hendrick’s goal was the 1,000th goal Chelsea had conceded in the Premier League. This goal earned him his second Goal of the Season award for the club.

On 14 September 2019, Hendrick scored in his 100th Premier League appearance for Burnley with a stoppage-time equaliser in a 1–1 draw at Brighton & Hove Albion. It had appeared that Hendrick was in Sean Dyche’s future plans as he had started 22 of Burnley’s 29 matches before the 2019–20 season was brought to a sudden halt because of the COVID-19 pandemic. However, on 23 June 2020, it was revealed that Hendrick had turned down an offer to stay at Burnley and would end his four-year stint at the club on the expiration of his contract on 30 June.

His second goal for Ireland came on 23 March 2019 with a 12-yard strike in the 49th minute of a 1–0 away triumph against Gibraltar in a Euro 2020 qualifying match. This goal ended Ireland’s drought of 446 minutes without finding the net in all competitions. Hendrick won his 50th cap for Ireland on 5 September 2019 in a 1–1 draw at home to Switzerland.

After leaving Burnley and having been linked to Italian clubs Milan and Roma, Hendrick decided to join fellow Premier League club Newcastle United on 24 August 2020 in a free transfer on a four-year deal. He described Newcastle as ‘a massive club’ and manager Steve Bruce hailed his new signing by saying: “He’s an experienced international footballer who can play all across the midfield so we welcome him aboard. He’ll be a big asset to us, on and off the pitch.”

He made his Newcastle debut in a 2–1 win over Barnsley in a pre-season friendly on 29 August 2020. Two weeks later, Hendrick scored and also set up a goal for Callum Wilson on his competitive debut for Newcastle in a 2–0 away win over West Ham United.