Party starts to go and eat with official (4)

I believe the answer is:

doge

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'official' is the definition.
(doge is a kind of official)

'party starts to go and eat' is the wordplay.
'party' becomes 'do' (do can informally mean a party).
'starts to' says to take the initial letters.
'and' is a charade indicator (letters next to each other).
'eat' becomes 'e' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
The first letter of 'go' is 'g'.
'do'+'g'+'e'='DOGE'

'with' is the link.

Can you help me to learn more?

(Other definitions for doge that I've seen before include "Title of former ruler of Venice" , "Chief of ancient Venice" , "Venetian leader" , "Historically, the chief magistrate of Venice or Genoa" , "Old ruler of Venice" .)

I've seen this clue in the Sydney Morning Herald.

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