Part of tribe quietly invading group (4)
I believe the answer is:
sept
'part of tribe' is the definition.
(a sept is a subdivision of a clan or tribe)
'quietly invading group' is the wordplay.
'quietly' becomes 'p' (p for piano and quiet).
'invading' means one lot of letters goes inside another.
'group' becomes 'set' (both can mean a collection).
'p' inserted within 'set' is 'SEPT'.
(Other definitions for sept that I've seen before include "Division of a tribe in Ireland or Scotland" , "Short month" , "Part of clan" , "Irish family group" , "Branch of Irish clan" .)