[8] In 2011, Jessup was cast as a main character in the TNT science fiction series Falling Skies.

[9] In 2012, Jessup starred in the Canadian independent film Blackbird, in which he played a troubled teen falsely accused of planning a school shooting.

[16] Jessup has stated in numerous interviews that his intention is to work in the film industry beyond acting, as a director and filmmaker.

[1] In 2017, it was announced that Jessup would be directing a documentary profile of Thai filmmaker Apichatpong Weerasethakul for FilmStruck and The Criterion Collection.

[3] In 2019, he produced the omnibus film 30/30 Vision: 3 Decades of Strand Releasing, which included short films by Ira Sachs, Catherine Breillat, Cindy Sherman, Athina Rachel Tsangari, Brady Corbet, Rithy Pahn, Lulu Wang and more.

[27] As a director, Jessup has expressed a particular fascination with Japanese film and culture and has stated in interviews that he is highly influenced by East Asian cinema, including directors Hirokazu Kore-eda, Edward Yang, Yasujirō Ozu, Hayao Miyazaki, Isao Takahata, and Apichatpong Weerasethakul.