Most of new school having walls painted (8)

I believe the answer is:

frescoed

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'painted' is the definition.
(frescoing is a kind of painting)

'most of new school' is the wordplay.
'most of' means to remove the last letter.
'new' becomes 'fresh' (associated in meaning).
'school' becomes 'coed' (a co-educational school).
'fresh' with its final letter taken off is 'fres'.
'fres'+'coed'='FRESCOED'

'having walls' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.

Can you help me to learn more?

I've seen this clue in The Times.

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