[2] Gammelby made his Danish 1st Division debut under head coach Jesper Sørensen on 27 March 2014 in a 1–0 win over Hobro IK, where he featured in the starting line-up at centre-back due to injuries to regular starters Simon Jakobsen and Thorbjørn Holst Rasmussen.

[9] During his first season in Brøndby, he struggled to make the starting lineup with head coach Alexander Zorniger preferring first Johan Larsson and since Kevin Mensah at the right back position.

[12] On 5 October 2020, transfer deadline day, Gammelby moved to Superliga rivals Lyngby Boldklub on a season-long loan with an option to buy.

On 17 August, he made his debut in the UEFA Champions League in a 2–1 away loss to Red Bull Salzburg in the first leg of the play-off round.

[20] Gammelby made his competitive return for Brøndby on 4 September 2022, as he was preferred as right-back by head coach Niels Frederiksen ahead of Sebastian Sebulonsen in a 2–0 league win against AC Horsens.