Backing study covering rats maybe doesn't matter (5,4)
I believe the answer is:
never mind
'doesn't matter' is the definition.
('never mind' means something doesn't matter)
'backing study covering rats maybe' is the wordplay.
'backing' says the letters should be written in reverse.
'study' becomes 'den' (I've seen this before).
'covering' indicates putting letters inside.
'rats maybe' becomes 'vermin' (rats are an example).
'den' backwards is 'ned'.
'ned' enclosing 'vermin' is 'NEVER MIND'.
(Other definitions for never mind that I've seen before include "It doesn't matter" , "Forget" , "who cares?" , "Don't worry" .)