Jessup began acting at the age of 11 as a child actor.
After various early jobs, including a role in a stage adaptation of The Full Monty, Jessup got a lead role in the children's television series The Saddle Club, for which he is also credited with conceptualizing the plot of one episode.
He served as executive producer for the independent film Amy George, which played at the 2011 Toronto International Film Festival.

In 2011, Jessup was cast as a main character in the TNT science fiction series Falling Skies.
He starred on the show for five seasons.

In 2012, Jessup starred in the Canadian independent film Blackbird, in which he played a troubled teen falsely accused of planning a school shooting.
Jessup's performance received positive reviews and the film won various awards, including the Best Canadian First Feature Film award at the 2012 Toronto International Film Festival.
The film won three awards at the Atlantic Film Festival and won the Vancouver International Film Festival award for Best Canadian Feature Film.
It also screened at the Cannes Film Festival.

In 2015, Jessup also starred in the feature film Closet Monster, which won the Best Canadian Film Award at the 2015 Toronto International Film Festival, and screened at various film festivals around the world, before subsequently being released nationwide in July 2016.

In 2016, Jessup starred in the Emmy-winning ABC series American Crime as Taylor Blaine.
His performance was praised by critics.
He returned for the third season as Coy Henson.

In 2018, Jessup was cast as Tyler Locke, one of the main roles in the Netflix series Locke & Key, an adaptation of Joe Hill and Gabriel Rodriguez's popular comic series of the same name.
Jessup began acting at the age of 11 as a child actor. After various early jobs, including a role in a stage adaptation of The Full Monty, Jessup got a lead role in the children's television series The Saddle Club, for which he is also credited with conceptualizing the plot of one episode. He served as executive producer for the independent film Amy George, which played at the 2011 Toronto International Film Festival.
In 2011, Jessup was cast as a main character in the TNT science fiction series Falling Skies. He starred on the show for five seasons.
In 2012, Jessup starred in the Canadian independent film Blackbird, in which he played a troubled teen falsely accused of planning a school shooting. Jessup's performance received positive reviews and the film won various awards, including the Best Canadian First Feature Film award at the 2012 Toronto International Film Festival. The film won three awards at the Atlantic Film Festival and won the Vancouver International Film Festival award for Best Canadian Feature Film. It also screened at the Cannes Film Festival.
In 2015, Jessup also starred in the feature film Closet Monster, which won the Best Canadian Film Award at the 2015 Toronto International Film Festival, and screened at various film festivals around the world, before subsequently being released nationwide in July 2016.
In 2016, Jessup starred in the Emmy-winning ABC series American Crime as Taylor Blaine. His performance was praised by critics. He returned for the third season as Coy Henson.
In 2018, Jessup was cast as Tyler Locke, one of the main roles in the Netflix series Locke & Key, an adaptation of Joe Hill and Gabriel Rodriguez's popular comic series of the same name.
Connor Jessup