A cover is a new performance of an existing composition, recorded without using or sampling the original recording. You are recreating the song not copying the audio so you do not need a sample clearance. 
 
However, the composition still belongs to the original songwriter(s). Traditionally, you could release a cover simply by obtaining the appropriate mechanical licence and ensuring the writers were credited and paid. 
 
But the landscape is changing. 
 
Today, many publishers and songwriters require advance approval before you release a cover, especially when: 
 
  *   The original writer has their own upcoming cover or remix planned 
 
  *   They want to control how and when the song reenters the market 
 
  *   They want to avoid multiple competing versions in the same space 
 
  *   The cover significantly changes the style, genre, or intended meaning 
 
  *   The release strategy of the original or its catalogue is sensitive or timespecific 
 
So while covers don’t involve the original recording and aren’t considered sampling, writers must still respect the composition rights and increasingly, this means that approval from the publisher and the original writers may be required. And they have no obligation to give permission, or even to give a reason for their refusal.