Wear a boring Briton's garment (6,4)
I believe the answer is:
sports coat
'garment' is the definition.
(sports coat is a kind of garment)
'wear a boring briton's' is the wordplay.
'wear' becomes 'sport' (I've seen this before).
'boring' means one lot of letters goes inside another (some letters must 'bore' a hole into other letters).
'briton' becomes 'scot'.
'a' going within 'scot' is 'scoat'.
'sport'+'scoat'='SPORTS-COAT'
(Other definitions for sports coat that I've seen before include "which can be put on" , "jacket" .)