The school head cried when given the brush off (5)

I believe the answer is:

swept

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'given the brush off' is the definition.
I can't judge whether this definition defines the answer.

'the school head cried' is the wordplay.
'head' suggests taking the first letters.
'cried' becomes 'wept' ('weep' can be a synonym of 'cry').
The initial letter of 'school' is 's'.
's'+'wept'='SWEPT'

'when' acts as a link.

Can you help me to learn more?

(Other definitions for swept that I've seen before include "Brushed up (dust)" , "what daily did" , "Removed by brushing" , "Was searcher" , "Cleaned by brushing" .)

I've seen this clue in the Evening Standard.

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