Closing university behind walls Cambridge University put up (8)
I believe the answer is:
ultimate
'closing' is the definition.
(thesaurus)
'university behind walls cambridge university put up' is the wordplay.
'university' becomes 'U' (abbreviation for university).
'behind' becomes 'late' (as in behind schedule).
'walls' is an insertion indicator (to 'wall' can mean to contain).
'cambridge university' becomes 'MIT' (MIT in Cambridge, Massachusetts).
'put up' says the letters should be written backwards.
'mit' in reverse letter order is 'tim'.
'late' going around 'tim' is 'ltimate'.
'u'+'ltimate'='ULTIMATE'
(Other definitions for ultimate that I've seen before include "The final point" , "Eventual" , "Utmost or extreme" , "Furthest, final" , "Last or highest" .)