Garment that's popular in the outskirts of Delhi (5)
I believe the answer is:
dhoti
'garment' is the definition.
(dhoti is a kind of garment)
'popular in the outskirts of delhi' is the wordplay.
'popular' becomes 'hot' ('hot' can be similar in meaning to 'popular').
'in the' means one lot of letters goes inside another.
'outskirts of' suggests removing the centre.
'delhi' with its middle removed is 'di'.
'hot' going into 'di' is 'DHOTI'.
'that's' is the link.
(Other definitions for dhoti that I've seen before include "garment in India" , "article of clothing" , "Simple Indian garment" , "Loincloth worn by Indians" , "pants in Goa?" .)