University, rather unorthodox, that's used by a peer (7)
I believe the answer is:
urethra
'that's used by a peer' is the definition.
(the urethra is used by somebody peeing, a 'peer')
'university rather unorthodox' is the wordplay.
'university' becomes 'u' (abbreviation for university).
'unorthodox' indicates anagramming the letters.
'rather' with letters rearranged gives 'rethra'.
'u'+'rethra'='URETHRA'
(Other definitions for urethra that I've seen before include "part of body" , "Canal from the bladder" , "wee channel" , "course of discharge" .)