Given not a penny in help! (3)

I believe the answer is:

aid

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'help' is the definition.
(synonyms)

'given not a penny in' is the wordplay.
'given' becomes 'a' (I can't justify this - if you can you should give a lot more credence to this answer).
'not' indicates named letters should be taken away.
'a' becomes 'amp' (A is the symbol for the amp or ampere).
'penny' becomes 'p' (short for pence).
'in' becomes 'amid'.
'p'+'amid'='pamid'
'pamid' with 'amp' taken out is 'id'.
'a'+'id'='AID'

Can you help me to learn more?

(Other definitions for aid that I've seen before include "encouragement" , "Care and help" , "Help. Assist" , "Auxiliary" , "charity" .)

I've seen this clue in the Evening Standard.

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