Family initially languishing in jail (4)
I believe the answer is:
clan
'family' is the definition.
(clan can mean a large family)
'initially languishing in jail' is the wordplay.
'initially' suggests taking the first letters.
'in' is an insertion indicator.
'jail' becomes 'can' (the can is American slang for prison).
The initial letter of 'languishing' is 'l'.
'l' placed into 'can' is 'CLAN'.
(Other definitions for clan that I've seen before include "(Scottish) family group" , "Group with a tartan?" , "Scots family group" , "Scots family grouping" , "Kinship group" .)