[11] In 2014, he starred as Tom Anderson in the holiday comedy Get Santa, and as a recurring character Archie Beckles in the CBBC series Rocket's Island.

[24][25] In April 2021, it was announced that Connor would star opposite Joe Locke in the Netflix series Heartstopper, an adaptation of the webcomic and graphic novel of the same name by Alice Oseman.

[27] In 2024 Connor was part of the voice cast of DreamWorks Animation's The Wild Robot, an adaptation of Peter Brown's novel of the same name.

[33] Connor will next star in an upcoming film adaptation of the novel A Cuban Girl's Guide to Tea and Tomorrow by Laura Taylor Namey.

[37][38][39] Connor has objected to speculation about his sexuality in the past[40][41] and had quit Twitter the previous month due to harassment and claims of queerbaiting after he was photographed holding hands with actress Maia Reficco.

[37] Many fans expressed support for Connor and criticised how people were treating him, as did Heartstopper creator Alice Oseman, co-stars Joe Locke, Sebastian Croft, Kizzy Edgell, and Olivia Colman, journalist Mark Harris, and Labour Party MP Nadia Whittome.