Shut, leaderless, small cafe sadly suffers blow to reputation (5,4)

I believe the answer is:

loses face

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'shut leaderless small' is the definition.
I know nothing about this answer so I can't tell whether this works.

'cafe sadly suffers blow to reputation' is the wordplay.
I cannot really understand how this works, but
an anagram of 'cafe' is 'face' which is located in the answer.
'suffers' could be 'loses' (losing is a kind of suffering) and 'loses' is found in the answer.
No letters remain.
This explanation may well be incorrect...

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