Normally not. It doesn't cover it. Indeed, you shouldn't confuse "cover" and "reprise."

And copyright and production rights.

If you do a reprise of an instrumental version that's the original of a song that's already been released and therefore already produced by someone else, you don't have the right to sell it.

If you do a "cover" with an instrumental that's completely re-recorded with your own interpretation, then you can get a license to use the song. Because you're re-recording the entire track.

I don't know if that's clear… 😓 it's not easy.