Like Rupert, possibly, in old city function (6)
I believe the answer is:
ursine
'like rupert possibly' is the definition.
(as in Rupert the Bear - ursine means like a bear)
'old city function' is the wordplay.
'old city' becomes 'ur' (ancient city state).
'function' becomes 'sine' (mathematical function).
'ur'+'sine'='URSINE'
'in' acts as a link.
(Other definitions for ursine that I've seen before include "Describing Pooh or Yogi?" , "like a character in 14 across [=>BEAR]" , "with grizzly features?" , "Bearlike" , "Like Paddington" .)