Pass over old American university (4)
I believe the answer is:
omit
'pass over' is the definition.
(thesaurus)
'old american university' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'american university' becomes 'mit' (I've seen this in other clues).
'o'+'mit'='OMIT'
(Other definitions for omit that I've seen before include "Fail to mention" , "Leave out or fail to do" , "Leave something out" , "Leave out or neglect" , "Exclude - neglect" .)