On September 28, 2015, the Chicago Bears traded Bostic to the New England Patriots in exchange for a sixth-round pick (204th overall) in the 2016 NFL Draft. Upon arriving to the New England Patriots, head coach Bill Belichick named Bostic the backup strongside linebacker behind Jamie Collins. On December 7, 2015, Bostic earned his first start as a member of the Patriots in place of Dont'a Hightower after Hightower sustained a shoulder injury. He recorded one tackle during a 27–6 victory at the Houston Texans in Week 14. He finished the 2015 season with two combined tackles (one solo) in 11 games and one start.