self-cover; new version of one's own song
Refers to an artist re-recording or rearranging their own previously released song, often in a different style. Common in Japanese music industry contexts.
wasei-eigo (Japanese-coined English), from self cover
His new album includes a self-cover of an old hit song.
songwriter's own performance of a song written for another artist
Used when a songwriter performs a song they originally wrote for someone else. Less common than sense 1, but understood in music circles.
This song was originally written for another singer, but this time I tried singing it myself as a self-cover.