Husband absorbed by observing a trifle (7)
I believe the answer is:
nothing
'a trifle' is the definition.
(thesaurus)
'husband absorbed by observing' is the wordplay.
'husband' becomes 'h'.
'absorbed by' means one lot of letters goes inside another.
'observing' becomes 'noting' ('note' can be a synonym of 'observe').
'h' put into 'noting' is 'NOTHING'.
(Other definitions for nothing that I've seen before include "Unimportant item" , "One of those sweet sayings" , "Not a whit" , "signifying love" , "Nought; of no value" .)