Arab city had broadcaster, full of energy, turned back (6)

I believe the answer is:

jeddah

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'arab city' is the definition.
I don't know anything about this answer so I cannot judge whether it can be defined by this definition.

'had broadcaster full of energy turned back' is the wordplay.
'broadcaster' becomes 'dj' (dj is a kind of broadcaster).
'full of' means one lot of letters goes inside another.
'energy' becomes 'e' (physics symbol as in E=mcj).
'turned back' is a reversal indicator.
'had'+'dj'='haddj'
'haddj' going around 'e' is 'haddej'.
'haddej' backwards is 'JEDDAH'.

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I've seen this clue in The Irish Times.

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