Hot food served up after dodgy starter in a German city (9)

I believe the answer is:

edinburgh

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'hot food served up' is the definition.
I can't tell whether this definition defines the answer.

'dodgy starter in a german city' is the wordplay.
'starter' indicates taking the first letters.
'in' indicates putting letters inside.
'a german' becomes 'ein' ('a' in German).
'city' becomes 'burgh' (I've seen this in another clue).
The initial letter of 'dodgy' is 'd'.
'd' placed inside 'ein' is 'edin'.
'edin'+'burgh'='EDINBURGH'

'after' acts as a link.

Can you help me to learn more?

(Other definitions for edinburgh that I've seen before include "Capital city of Scotland" , "Scottish arts festival city" , "town" , "Scotland's capital" , "fringe city" .)

I've seen this clue in The Daily Express.

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