Dress of southern Asia — round India, primarily (4)
I believe the answer is:
sari
'dress' is the definition.
(I know that sari is a type of dress)
'southern asia round india primarily' is the wordplay.
'primarily' suggests taking the first letters.
The initial letters of 'southern asia round india' is 'SARI'.
'of' is the link.
(Other definitions for sari that I've seen before include "Something worn" , "Hindu female garment" , "Traditional Indian garment" , "Indian robe" , "Hindu woman's dress" .)