Crossword Genius

Mostly support a sort of posh cafe (3,4)


I believe the answer is:

tea shop

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

'cafe' is the definition.
(I've seen this before)

'mostly support a sort of posh' is the wordplay.
I cannot quite understand how this works, but
'support' could be 'shop' (shopping is a kind of supporting) and 'shop' is present in the answer.
'a' is within the answer.
The remaining letters 'te' is a valid word which might be clued in a way I don't understand.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

(Other definitions for tea shop that I've seen before include "refreshing facility" , "Refreshments provider" , "Cafe (paradoxically?)" , "Restaurant serving light meals" , "Small cafe" .)

I've seen this clue in The Telegraph.
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