A test for mother? Not her! (3)
I believe the answer is:
mot
'a test' is the definition.
(as in an MOT test for a vehicle)
'mother? not her' is the wordplay.
'not' is a deletion indicator.
'mother' with 'her' taken away is 'MOT'.
'for' is the link.
(Other definitions for mot that I've seen before include "Witty saying" , "Wisecrack (for older cars!)" , "Clever remark" , "French word for Tom" , "Irish girlfriend" .)