Shield university kept in battered chest once (10)
I believe the answer is:
escutcheon
'shield' is the definition.
(escutcheon is a kind of shield)
'university kept in battered chest once' is the wordplay.
'university' becomes 'u'.
'kept in' is an insertion indicator.
'battered' indicates anagramming the letters.
'chest'+'once'='chestonce'
'chestonce' is an anagram of 'esctcheon'.
'u' placed inside 'esctcheon' is 'ESCUTCHEON'.
(Other definitions for escutcheon that I've seen before include "Family shield" , "Heraldic emblem" , "Heraldic shield" .)