Like some universities, say, breaking random local tie (10)
I believe the answer is:
collegiate
'like some universities' is the definition.
(some universities are collegiate)
'say breaking random local tie' is the wordplay.
'say' becomes 'eg' (both can mean for example).
'breaking' indicates putting letters inside.
'random' is an anagram indicator.
'local'+'tie'='localtie'
'localtie' anagrammed gives 'colliate'.
'eg' inserted within 'colliate' is 'COLLEGIATE'.
(Other definitions for collegiate that I've seen before include "Constituted like Oxford or Cambridge universities" , "in institution" , "Relating to a particular group of students" , "educational establishment" .)