As a youth, Clendening played in the 2004 Quebec International Pee-Wee Hockey Tournament with a minor ice hockey team from Rochester, New York. Prior to his professional career, he played for Boston University, and played hockey in Canada for the Toronto Marlboros' AAA junior team. Clendening was part of Team USA's gold-medal-winning team at the 2010 IIHF World U18 Championships. During the tournament he led all defensemen with 10 points, and tied for the lead among defensemen with 3 goals and 7 assists. His 10 points ranked 6th among all players in the tournament, and his 7 assists ranked 4th. He was named as one of the defensemen to the tournament all-star team and as one of Team USA's 3 top players.
On January 29, 2015, the Blackhawks traded Clendening to the Vancouver Canucks in exchange for Gustav Forsling. Clendening finished out the season appearing in 17 games for the Canucks, as well as 11 games for the Utica Comets.
On July 28, 2015, Clendening, along with Nick Bonino and a 2nd-round pick in the 2016 NHL Entry Draft were traded from the Canucks to the Pittsburgh Penguins in exchange for Brandon Sutter and a 3rd-round pick in the 2016 NHL Entry Draft. Clendening made the Penguins roster to open the 2015–16 season, and would appear in 9 games for the club, as well as 6 for the Wilkes-Barre/Scranton Penguins.
On January 16, 2016, Clendening was included in yet another trade, being sent to the Anaheim Ducks alongside David Perron in exchange for Carl Hagelin. However, Clendening's time with the Ducks was short-lived, as he was claimed off waivers by the Edmonton Oilers two weeks later on January 27. This marked the fifth organization Clendening would join within the year, though he never actually played a game whilst with the Ducks. Clendening skated in 20 games for the Oilers, recording 1 goal and 6 points.
On July 1, 2016, Clendening signed as a free agent to a one-year, two-way contract with the New York Rangers. Clendening appeared in 31 games for the Rangers, scoring 11 points.
On July 1, 2017, Clendening signed a one-year, one-way contract as a free agent with the Arizona Coyotes. Having made the Coyotes opening night roster for the 2017–18 season, Clendening only appeared in 5 games for the team before he was placed on waivers and reassigned to play 21 games for the Tucson Roadrunners of the AHL. On January 10, 2018, Clendening, alongside Anthony Duclair was traded to the Blackhawks in exchange for Richard Pánik and Laurent Dauphin, returning to Chicago for a second stint. He was immediately assigned to play out the remainder of the season with the Rockford IceHogs of the AHL.
Columbus Blue Jackets
As a free agent from the Blackhawks, Clendening left to sign a one-year, two-way contract with the Columbus Blue Jackets on July 1, 2018. He began the 2018–19 season on the Blue Jackets opening night roster, featuring in 4 games before he was placed on waivers and reassigned to AHL affiliate, the Cleveland Monsters. Leading the Monsters blueline in scoring, Clendening posted 4 goals and 37 points in 45 games, before he was recalled by Columbus to add depth for the playoffs. He made his NHL playoff debut with the Blue Jackets, appearing in game 3 of the Eastern Conference Quarterfinals against the Tampa Bay Lightning. He went on to collect an assist in 7 games before ending his season in the Conference Semifinals to the Boston Bruins. On June 25, 2019, Clendening was re-signed to a two-year $1.4 million contract extension with the Columbus Blue Jackets.
