Exclude from old American university (4)
I believe the answer is:
omit
'exclude' is the definition.
(I know that exclude can be written as omit)
'old american university' is the wordplay.
'old' becomes 'o' (abbreviation).
'american university' becomes 'MIT' (Massachusetts Institute of Technology).
'o'+'mit'='OMIT'
'from' is the link.
(Other definitions for omit that I've seen before include "Leave out, perhaps in error" , "Leave out or neglect" , "Leave out or overlook" , "Neglect to include" , "Exclude - neglect" .)