British family touring island, primarily introducing swimwear (6)
I believe the answer is:
bikini
'swimwear' is the definition.
(I've seen this before)
'british family touring island primarily introducing' is the wordplay.
'british' becomes 'b' (abbreviation e.g. in 'BBC').
'family' becomes 'kin' (synonyms).
'touring' is an insertion indicator (tour can mean to go around).
'island' becomes 'i' (geographical abbreviation).
'primarily' suggests taking the first letters.
The first letter of 'introducing' is 'i'.
'b'+'kin'='bkin'
'bkin' placed around 'i' is 'bikin'.
'bikin'+'i'='BIKINI'
(Other definitions for bikini that I've seen before include "Small two-piece bathing costume" , "Infamous atoll" , "Brief two-piece swimming costume" , "Skimpy garment" , "A small two -piece bathing costume" .)