Brought up gossip about husband's sexual activity (4)
I believe the answer is:
shag
'sexual activity' is the definition.
(shag is a kind of sexual activity)
'brought up gossip about husband's' is the wordplay.
'brought up' says the letters should be written in reverse (down clues only).
'gossip' becomes 'gas' (I've seen this before).
'about' is an insertion indicator.
'husband' becomes 'h'.
'gas' placed around 'h' is 'gahs'.
'gahs' in reverse letter order is 'SHAG'.
(Other definitions for shag that I've seen before include "Kind of cormorant - tobacco" , "Coarse tobacco - cormorant" , "Green cormorant" , "Diver" , "Bird - dance" .)