One on a peg in the flat? (4,3)

I believe the answer is:

felt hat

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'one on a peg' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Perhaps you can see a link between them that I don't see?

'the flat?' is the wordplay.
'the flat' anagrams to 'FELT HAT'.
But, I'm unsure how this is indicated.

'in' acts as a link.

Can you help me to learn more?

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