In 2009, in a non-first-class match, McClenaghan took 5/36 against the England Lions for New Zealand Emerging Players.

It was announced on 14 June 2013 that he would be joining Lancashire as an overseas player for their Friends Life t20 campaign. He won the Man of the Match award in his first home match at Old Trafford against Nottinghamshire after taking 5 wickets for just 29 runs, although Lancashire still lost the game.

On 19 May 2015, he joined Middlesex as an overseas player for their final six T20 Blast group matches. McClenaghan replaced South Africa bowler Kyle Abbott at Lord’s from the end of June. He made his debut against Sussex at Lord’s on Thursday, 2 July, and took eight wickets in four appearances, including 3–24 from 4 overs on his debut. He was picked by the Lahore Qalandars for the third edition of the Pakistan Super League.

McClenaghan made his IPL debut in 2015, when he was bought by Mumbai Indians for 30 lakh. He went on to take 14 wickets at an average of 22.50 in 10 appearances in the tournament. He also played with the franchise in the 2016 and 2017 editions. After going unsold in the 2018 auction, McClenaghan was selected by the Mumbai Indians as a replacement for the injured Jason Behrendorff.

In September 2018, he was named in Nangarhar’s squad in the first edition of the Afghanistan Premier League tournament. In July 2019, he was selected to play for the Belfast Titans in the inaugural edition of the Euro T20 Slam cricket tournament. However, the following month the tournament was cancelled.