Quinn's previous television roles include the following:
- Arthur Havisham in Dickensian (BBC One)
- Leonard Blast in Howards End (BBC One & Starz)
- Tsarevich Pavel in Catherine the Great (HBO & Sky Atlantic)
- Billy Knight in Strike (BBC One)
- Enjolras in Les Misérables (BBC One)
- Koner (Stark soldier) in Game of Thrones (HBO)
Quinn also appeared in the film Make Up, which premiered at the 2019 BFI London Film Festival, in the role of Tom, the long term boyfriend of Ruth, the film's protagonist (played by Molly Windsor).
He has also appeared in a number of stage productions, including Deathwatch (Maurice), WISH LIST (Dean Carmody), and Mosquitos (Luke).
Quinn has been an actor since he was very young, saying, "I did it since I was a baby, in nursery I did a school play. I was a drama scholar at my school, so I got money off my fees on the condition I did acting" in a NUIT Magazine article.
He went to the London Academy of Music and Dramatic Art (LAMDA).
- When asked who he would want to play if he could choose to be in a remake of any classic movie or show, Quinn said he would like to be "all the characters in the Lord of the Rings trilogy." Another time when asked, "What’s the one role that you wish you had played?", Quinn pointed to Kieran Culkin's portrayal of Roman Roy in Succession as "enviable," stating, "These iconic roles are so defined by the actors that played them its hard to imagine anyone else playing them."
- It seems that Quinn previously had a public twitter account (@_joe_quinn), which has since been deleted. He has no other known public social media.