Caught duster on bit of rock (4)

I believe the answer is:

crag

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'bit of rock' is the definition.
'crag' can be an answer for 'rock' (I've seen this before). I'm unsure of the 'bit of' bit.

'caught duster on' is the wordplay.
'caught' becomes 'c' (cricket abbreviation).
'duster' becomes 'rag' (I've seen this in another clue).
'on' says to put letters next to each other.
'c'+'rag'='CRAG'

Can you help me to learn more?

(Other definitions for crag that I've seen before include "Rugged rock face" , "Avant-garde" , "Rocky hilltop" , "Steep or rugged cliff face" , "Steep rock, peak" .)

I've seen this clue in The Mirror.

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