On 30 May 2014, Izaguirre signed a new contract with Celtic, keeping him at the club until 2017. In the 2015–16 season, he was displaced as first-choice left back by 18-year-old Kieran Tierney. Despite what looked like an emotional farewell after the final game of the season against Motherwell on 15 May 2016, Izaguirre told Honduras website "La Prensa" that he still had a contract to see out and had not had any discussions with the Celtic board. He returned to Celtic for the 2016–17 season and played 12 games, covering for Tierney when the latter was injured.