Hendry played during his youth at Celtic, Peterborough and Dundee. He began his professional career at Scottish club Partick Thistle, where he made his debut in the top Scottish league on the final matchday of 2014/15. The central defender then moved to English club Wigan Athletic, which loaned him out to Shrewsbury Town and MK Dons. In the summer of 2017, he permanently joined Dundee United back in his home country, where he became a key player.
In 2018, the young Scot was signed by Celtic, but he only made fifteen appearances there. He then had two loan spells: first with Melbourne City in Australia and then with KV Oostende. Hendry had an outstanding season with KV Oostende, leading to his permanent transfer in the summer of 2021.
Only two months later, on 31 August 2021, Club Brugge signed the Scottish defender for €4.5 million. Hendry quickly established himself as a key player in both the domestic league and the Champions League. However, in 2022/23, Hendry found limited playing time at Blauw-Zwart, which led to a loan move to Italian promoted side Cremonese. During the mid-season break, Club Brugge decided to bring the Scottish player back to Jan Breydel. Jack Hendry's contract with Club Brugge runs until 2025.