Garment originally seen around Rajasthan institutions (4)
I believe the answer is:
sari
'garment' is the definition.
(I know that sari is a type of garment)
'originally seen around rajasthan institutions' is the wordplay.
'originally' indicates taking the first letters.
The first letters of 'seen around rajasthan institutions' is 'SARI'.
(Other definitions for sari that I've seen before include "Traditional dress of Indian women" , "Asian dress" , "Eastern garment" , "Indian robe" , "habit" .)