A little strap on choirmaster's garment (6)
I believe the answer is:
poncho
'garment' is the definition.
(poncho is a kind of garment)
'a little strap on choirmaster's' is the wordplay.
'a little' indicates a hidden word (a little bit of the clue).
'PONCHO' is hidden within 'strap on choirmaster'.
(Other definitions for poncho that I've seen before include "A blanket-like cloak with a hole in the centre for the head" , "Blanket-like cloak with slit for head" , "Blanket-like cloth with centre slit, worn as cloak" , "Kind of blanket with hole for head" , "Kind of cloak like blanket with slit for head" .)