In 2014, he was part of the ensemble in the revival of King Lear starring John Lithgow, Annette Bening and Yahya Abdul-Mateen II.

Burnap starred opposite Phillipa Soo as Guinevere in the revival with a new book by Aaron Sorkin.

Later that year, he portrayed Joris Ivens in the off-Broadway play Spain written by Jen Silverman, where he acted opposite Marin Ireland.

The play revolves around the complications of filming a movie financed by the Russian government during the Spanish Civil War.

[4] He is set to appear in the live-action Disney remake Snow White, starring opposite Rachel Zegler and Gal Gadot.