Old city is favourite with artist (5)
I believe the answer is:
petra
'old city' is the definition.
(I've seen this before)
'favourite with artist' is the wordplay.
'favourite' becomes 'pet' ('pet' can be a synonym of 'favourite').
'with' means one lot of letters go next to another.
'artist' becomes 'ra' (Royal Academician, member of Royal Academy of Arts).
'pet'+'ra'='PETRA'
'is' acts as a link.
(Other definitions for petra that I've seen before include "Picturesque city" , "Rock-hewn city of Jordan" , "Long-lost city of Jordan rediscovered in 1812" , "Ancient Jordanian city carved from rock" , "Burgon's rose-red city" .)