Starts to boost intimate relations with one's skimpy garment (6)
I believe the answer is:
bikini
'skimpy garment' is the definition.
(I've seen this before)
'starts to boost intimate relations with one's' is the wordplay.
'starts to' suggests taking the first letters.
'relations' becomes 'kin' (both can mean one's family).
'with' says to put letters next to each other.
'one' becomes 'i' (Roman numeral).
The initial letters of 'boost intimate' is 'bi'.
'bi'+'kin'+'i'='BIKINI'
(Other definitions for bikini that I've seen before include "Small two-piece bathing costume" , "Site of A-Bomb tests; resultantly shocking swimwear!" , "Skimpy garment" , "Kind of swimsuit" , "What holidaymaker may assume" .)