Fat geese periodically fed husband (4)
I believe the answer is:
ghee
'fat' is the definition.
(thesaurus)
'geese periodically fed husband' is the wordplay.
'periodically' means one should take alternating letters (letters must be selected 'every so often').
'fed' is an insertion indicator (one word is 'fed' to another).
'husband' becomes 'h' (abbreviation).
The alternating letters of 'geese' are 'gee'.
'gee' placed around 'h' is 'GHEE'.
(Other definitions for ghee that I've seen before include "clarified product" , "Clarified butter sauce" , "Form of clarified butter" , "type of butter" , "Indian form of butter" .)