Crossword Genius

Everyone in historic city beginning to transmit good wishes (3,3,4)

Ross

I believe the answer is:

all the best

I'm a little stuck... Click here to teach me more about this clue!

'transmit good wishes' is the definition.
I can't judge whether this definition defines the answer.

'everyone in historic city beginning to' is the wordplay.
'everyone' becomes 'all' (all people).
'in historic city' becomes 'thebes' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'beginning' suggests taking the first letters.
The first letter of 'to' is 't'.
'all'+'thebes'+'t'='ALL THE BEST'

Can you help me to learn more?

(Other definitions for all the best that I've seen before include "Without exception, unsurpassed" , "needing good luck!" , "Good health!" , "Pick of the bunch" , "flower, every bit of it?" .)

I've seen this clue in The Independent.
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