Fail to include old Cambridge seat of learning (4)
I believe the answer is:
omit
'fail to include' is the definition.
(I've seen this before)
'old cambridge seat of learning' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'cambridge seat of learning' becomes 'mit' (Massachusetts Institute of Technology in Cambridge).
'o'+'mit'='OMIT'
(Other definitions for omit that I've seen before include "Leave out or neglect" , "Skip" , "Fail to use" , "Leave out, do not include (4)" , "Disregard" .)