Asian shot in front of Princeton University (7)
I believe the answer is:
punjabi
'asian' is the definition.
(I've seen this before)
'shot in front of princeton university' is the wordplay.
'shot' becomes 'jab' (both can mean an injection).
'in' means one lot of letters goes inside another.
'front of' suggests taking the first letters (the letter at the front of the word).
'university' becomes 'uni' (informal abbreviation).
The first letter of 'princeton' is 'p'.
'p'+'uni'='puni'
'jab' going into '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?" .)