

In the US, the cover (as long as it doesn’t mess up the song too much) is automatically allowed, as long as you pay what is called a compulsory royalty (a certain amount per record sold, or per audience member in case of a live performance). ASCAP and/or the Harry Fox Agency (iirc) act among other things as clearinghouses for these payments. You have to notify them ahead of time of the cover you’re releasing, and maybe pay something up front.
Normally if you seek permission from the publisher of the song you want to cover, it’s because you want to negotiate a lower royalty than the compulsory one. You can often do that if you can convince them that your record is going to sell a lot of copies. It’s just a discussion about money and business people are used to that.
If your performance copies from the original but is not a straightforward cover, then you do need permission ahead of time as the compulsory license doesn’t apply, with some limited free-speech exceptions for parodies.
IANAL bla bla bla.
https://en.wikipedia.org/wiki/Compulsory_license#United_States







Looks lame, and stupid expensive.