While not a psychological horror film, Whiplash (2014)is a psychological drama about a drummer named Andrew Neiman as he studies his craft under Terence Fletcher.
Suspiria (2018) fully leans into its horror aspect by having a supernatural element. It is a little gorier than Black Swan as it features themes of body horror.
The Perfection (2018) is centered on the rivalry between Charlotte Willmore and Elizabeth Wells, two cellists vying for a spot of honor in Bachoff, a prestigious music school.