Flap in the manner of a bat (3)

I believe the answer is:

tab

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'flap in the manner' is the definition.
'tab' can be an answer for 'flap' (both can mean a small piece of material). I'm unsure of the 'in the manner' bit.

'of a bat' is the wordplay.
'of' is an anagram indicator (the answer comes from or 'of' the letters).
'bat' anagrammed gives 'TAB'.

Can you help me to learn more?

(Other definitions for tab that I've seen before include "The bill in a restaurant" , "Running bar bill" , "Flap; meal bill" , "Small flap - bill" , "Marker" .)

I've seen this clue in the Evening Standard.

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