Asian shot in front of Princeton University (7)
I believe the answer is:
punjabi
'asian' is the definition.
(I know that Punjabi is a type of Indian)
'shot in front of princeton university' is the wordplay.
'shot' becomes 'jab' (both can mean an injection).
'in' indicates putting letters inside.
'front of' suggests taking the first letters.
'university' becomes 'uni' (I've seen this before).
The initial letter of 'princeton' is 'p'.
'p'+'uni'='puni'
'jab' put within 'puni' is 'PUNJABI'.
(Other definitions for punjabi that I've seen before include "From a state in Northwest India" , "Asian language" , "foreign language" , "tongue" , "talk of Amritsar?" .)