Tough woman keeps family notice (8)
I believe the answer is:
skinhead
'tough' is the definition.
(I know that skinhead is a type of tough)
'woman keeps family notice' is the wordplay.
'woman' becomes 'she' ().
'keeps' is an insertion indicator (inserted letters are kept inside).
'family' becomes 'kin' (synonyms).
'notice' becomes 'ad' (both can mean an advertisement).
'she' placed around 'kin' is 'skinhe'.
'skinhe'+'ad'='SKINHEAD'
(Other definitions for skinhead that I've seen before include "1970s British white racist" , "Punk" , "Ruffian" , "Shaven-headed youth" , "The scalp" .)