An old-fashioned garment lingers on (5)
I believe the answer is:
stays
This might be a double definition.
'an old-fashioned garment' is the first definition.
'stays' can be an answer for 'garment' (stays is a kind of garment). I am not certain of the 'an old-fashioned' bit.
'lingers on' is the second definition.
'stays' can be an answer for 'lingers' (I've seen this in another clue). I'm unsure of the 'on' bit.
Can you help me to learn more?
(Other definitions for stays that I've seen before include "old underwear" , "Boards, lodges" , "Supports" , "restrictive garments" , "Settles" .)