What it costs to go to finishing school, we believe (4)

I believe the answer is:

feel

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'believe' is the definition.
(I know that feel is a more specific form of believe)

'what it costs to go to finishing school we' is the wordplay.
'what it costs' becomes 'fe' (I can't explain this - if you can you should believe this answer much more).
'to go' indicates anagramming the letters (I've seen 'went' mean this ('go' can mean move)).
'to finishing' suggests the final letters (the letter which finishes the word).
The final letters of 'school we' are 'le'.
'le' is an anagram of 'el'.
'fe'+'el'='FEEL'

Can you help me to learn more?

(Other definitions for feel that I've seen before include "Have a belief; touch" , "16A [JUDGE]" , "Find by groping" , "Leg (of mutton/lamb)" , "Perceive, sense" .)

I've seen this clue in the Evening Standard.

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