Member of family admits love willingly (4)
I believe the answer is:
soon
'willingly' is the definition.
(thesaurus)
'member of family admits love' is the wordplay.
'member of family' becomes 'son'.
'admits' is an insertion indicator.
'love' becomes 'o' (In tennis, 'love' means 'zero').
'son' going around 'o' is 'SOON'.
(Other definitions for soon that I've seen before include "in a minute" , "Early; readily" , "In the near future" , "Before you can say Jack Robinson" , "Shortly" .)