Damage done by central Sahara vermin (4)

I believe the answer is:

harm

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'damage' is the definition.
(synonyms)

'central sahara vermin' is the wordplay.
'central' indicates the central letters.
'vermin' becomes 'rm' (I can't justify this - if you can you should give a lot more credence to this answer).
The central letters of 'sahara' are 'ha'.
'ha'+'rm'='HARM'

'done by' is the link.

Can you help me to learn more?

(Other definitions for harm that I've seen before include "Hurt, maim" , "Detriment" , "Injure or damage" , "See 13" , "Injure, injury" .)

I've seen this clue in The Irish Times.

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