Mother doesn't need her for a test (3)
I believe the answer is:
mot
'test' is the definition.
(as in an MOT test for a vehicle)
'mother doesn't need her' is the wordplay.
'doesn't need' suggests deleting specific letters.
'mother' with 'her' taken out is 'MOT'.
'for a' acts as a link.
(Other definitions for mot that I've seen before include "type of test" , "French word for Tom" , "witty remark" , "Vehicle check" , "Word in France, bon perhaps" .)