Content to leave education -- American university, Yale's heading for feud (6)
I believe the answer is:
enmity
'feud' is the definition.
(thesaurus)
'content to leave education american university yale's heading' is the wordplay.
'content to leave' suggests removing the centre (the contents of the word are removed).
'american university' becomes 'MIT' (Massachusetts Institute of Technology).
'heading' suggests taking the first letters (head could mean the top letter).
'education' with its middle taken out is 'en'.
The initial letter of 'yales' is 'y'.
'en'+'mit'+'y'='ENMITY'
'for' acts as a link.
(Other definitions for enmity that I've seen before include "discord" , "Hate; aversion" , "evident in time?" , "Hatred, hostility" , "Hostility, bad feeling towards" .)