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Here's one from the cryptic in my local:-
"HEADGEAR SPORTED BY ONE GOING THROUGH
LEICESTER, SAY" (12)
C-H-S-C-T E-
I cannot be sure about the first two letters supplied.

I've just thought, is there a hat called a cheesecutter?

I'm answering my own query here, but I see
that a cheese cutter is a type of cap,

Bingo.

In Chambers :
A square-peaked cap (nautical).

Not sure about the LEICESTER connection.

Of course, one cutting the cheese. (-;