Worry about Gath, troubled old city (8)
I believe the answer is:
carthage
'old city' is the definition.
(I've seen this before)
'worry about gath troubled' is the wordplay.
'worry' becomes 'care' (eg without a care means without a worry).
'about' means one lot of letters goes inside another.
'troubled' indicates anagramming the letters.
'gath' with letters rearranged gives 'thag'.
'care' going around 'thag' is 'CARTHAGE'.
(Other definitions for carthage that I've seen before include "Dido was queen of this ancient city in N Africa" , "Old African city" , "Chart age of Dido's ancient city" , "Phoenician city state near modern Tunis" , "Ancient Tunisian city" .)