Dashing family mostly involved in outbreak (6)
I believe the answer is:
rakish
'dashing' is the definition.
(synonyms)
'family mostly involved in outbreak' is the wordplay.
'family' becomes 'kin' (synonyms).
'mostly' means to remove the last letter.
'involved in' means one lot of letters goes inside another.
'outbreak' becomes 'rash' (rash can mean a sudden outbreak).
'kin' with its final letter taken away is 'ki'.
'ki' inserted within 'rash' is 'RAKISH'.
(Other definitions for rakish that I've seen before include "Dashing and slightly disreputable" , "Dapper" , "Dashing, devil-may-care" , "Jaunty; fast-looking (boat)" , "abandoned" .)