Mother checks out but doesn't leave (7)
I believe the answer is:
remains
'doesn't leave' is the definition.
(I've seen this in another clue)
'mother checks out' is the wordplay.
'mother' becomes 'ma' (ma can mean mother).
'checks' becomes 'reins' (reining is a kind of checking).
'out' means one lot of letters goes inside another.
'ma' placed inside 'reins' is 'REMAINS'.
'but' is the link.
(Other definitions for remains that I've seen before include "Stays; dead body" , "Residue" , "What's left (maybe of a body)" , "Scraps" , "Leftovers" .)