Love missing husband, not that she regrets (4)
I believe the answer is:
otis
'she regrets' is the definition.
(reference to the song Miss Otis Regrets)
'love missing husband not that' is the wordplay.
'love' becomes 'o' (In tennis, 'love' means 'zero').
'missing' suggests deleting specific letters.
'husband' becomes 'h'.
'not that' becomes 'this' (I've seen this before).
'this' with 'h' removed is 'tis'.
'o'+'tis'='OTIS'
(Other definitions for otis that I've seen before include "Regretful miss" , "- - Redding (soul music star)" , "---- Redding, 1941-67, soul singer" , "Place of worship; side part of head" , "Miss -- Regrets, Cole Porter song" .)