Censor lady cut short (4)

I believe the answer is:

edit

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'censor' is the definition.
(thesaurus)

'lady cut short' is the wordplay.
'lady' becomes 'edi'.
'cut short' becomes 't' (I can't explain this - if you can you should believe this answer much more).
'edi'+'t'='EDIT'

Can you help me to learn more?

(Other definitions for edit that I've seen before include "amend copy" , "Revise for publication" , "Check text for publication" , "Make textual changes" , "Supervise - amend" .)

I've seen this clue in The Telegraph.

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