Amaro was named a semi-finalist for the John Mackey and Fred Biletnikoff Awards in November, becoming the first player to be listed for both awards since Missouri’s Chase Coffman in 2008. Amaro was also named a finalist for the Earl Campbell Tyler Rose Award, given to the best offensive player with Texas ties. On November 25, 2013, it was announced that Amaro was not named a finalist for the Mackey Award, given to the best tight end in college football, leading several media personalities including CBS Sports writer Dennis Dodd to criticize the Award’s validity. At the point at which the finalist list was announced, Amaro had only 16 fewer receptions than the three finalists combined.

Amaro sufficiently recovered from his injury to appear in the 2012 Meineke Car Care Bowl of Texas against Minnesota, in which he was ejected for punching a defender. Due to his earlier injury, Amaro had been unable to practice until the week of the game.

Amaro attended Texas Tech University from 2011 to 2013. During his college career, he earned Unanimous All-American honors and set the record for Division I (NCAA) single season receiving yards by a tight end in 2013.

Amaro broke the 1,000 receiving yards mark following a loss to Oklahoma State on November 2, 2013. Amaro exceeded his career receptions and reception yard highs with 15 and 174 respectively, and was two receptions shy of tying the NCAA single-game record for receptions by a tight end. In the following games against Kansas State and Baylor, Amaro received significant injuries. A hit during the Kansas State game forced him to be carted off the field, before later returning briefly. In the subsequent game against Baylor, Amaro received a high hit to the shoulder from safety Ahmad Dixon. The hit required Amaro to again return to the locker room with an injury.

Amaro completed the regular season 90 yards and 14 receptions short of setting NCAA FBS records for single season tight end receiving yards and receptions, with an opportunity to set the records in an appearance in the 2013 Holiday Bowl. Amaro broke the single season tight end receiving record during the game, and finished his Holiday Bowl performance with 8 receptions and 112 yards. With the completion of the season, Amaro’s 104 receiving yards per game also set an NCAA single season record for the tight end position.

The Associated Press and Big 12 Coaches named Amaro a unanimous 2013 All-Big 12 first team selection on December 9, 2013. He was additionally named a 1st Team All-American at the tight end position by Bleacher Report, USA Today, CBS Sports, Sporting News, Athlon Sports, SB Nation, the Associated Press, Sports Illustrated and the Walter Camp Foundation. Amaro became a Unanimous All-American with his 1st team selection by the American Football Coaches Association and the Football Writers Association of America on December 18, 2013, the first Red Raider to earn the honor since Michael Crabtree in 2008. Only 5 Red Raiders overall have earned unanimous All-American honors: Mark Bounds in 1991, Zach Thomas in 1995, Byron Hanspard in 1996, and Michael Crabtree in 2007-08.

Amaro was selected 49th overall by the New York Jets and was the second tight end selected. He was signed on May 16, 2014. In his rookie year of 2014, Amaro had 345 receiving yards on 38 receptions in 14 games.

On September 1, 2015, it was revealed that Amaro had a torn labrum, an injury since he landed awkwardly during the first preseason game against the Lions. The injury required surgery, prematurely ending his 2015 season.

The Jets waived Amaro on September 3, 2016 for final roster cuts before the start of the season. He is considered to be another on a long list of disappointing draft picks for the jets.

Amaro was claimed off waivers by the Tennessee Titans on September 4, 2016.

He started his first year with the Titans as their third tight end on their depth chart, behind veterans Delanie Walker and Anthony Fasano. On September 25, 2016, Amaro made his debut with the Tennessee Titans and made three receptions for 59 receiving yards in a 10-17 loss to the Oakland Raiders.

On September 2, 2017, Amaro was waived by the Titans.

On January 9, 2018, Amaro signed a reserve/future contract with the Kansas City Chiefs. He was released on September 1, 2018.