Ancient city part destroyed out East (5)
I believe the answer is:
petra
'ancient city' is the definition.
(I've seen this before)
'part destroyed out east' is the wordplay.
'destroyed' indicates an anagram.
'out' is an insertion indicator.
'east' becomes 'e' (abbreviation).
'part' anagrammed gives 'ptra'.
'ptra' enclosing 'e' is 'PETRA'.
(Other definitions for petra that I've seen before include "Long-lost city of Jordan rediscovered in 1812" , "Rock-hewn city of Jordan" , "Jordan's rock-hewn city" , "A rose-red city - 'half as old as Time'! (Burgon)" , "Old city in Jordan" .)