Celebrity caught up in The Mafia (4)
I believe the answer is:
fame
'celebrity' is the definition.
(celebrity can mean the quality of being famous)
'caught up in the mafia' is the wordplay.
'caught up' is a reversal indicator (in a down clue, letters go up).
'in' indicates a hidden word.
'emaf' can be found hidden inside 'the mafia'.
'emaf' written backwards gives 'FAME'.
(Other definitions for fame that I've seen before include "Musical - stardom" , "Renown, celebrity" , "Celebrity; stage musical" , "Notoriety or celebrity" , "Note" .)