Yes, Jarman did make music videos. One of his most notable music videos is for the song "Freedom!'90" by George Michael, which features Jarman as a character called "Mr. Man". The video is a surreal and highly stylized depiction of the AIDS crisis, and it was highly controversial at the time of its release.
Unveiling Derek Jarman: A Cinematic Journey through the Life and Works of a British Mastermind