Short cut out of Battersea (5)

I believe the answer is:

terse

I'm a little stuck... Click here to teach me more about this clue!

'short cut out' is the definition.
'terse' can be an answer for 'short' (terse can mean short or brusque). I'm not sure about the 'cut out' bit.

'of battersea' is the wordplay.
'of' indicates the answer is hidden within the clue.
'TERSE' is hidden within 'battersea'.

Can you help me to learn more?

(Other definitions for terse that I've seen before include "Succinct about trees" , "Curt, concise" , "Curt, laconic of speech" , "Brusque, concise" , "Crisply brief" .)

I've seen this clue in the Evening Standard.

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