Either sell, or give, the cat to (4)

I believe the answer is:

flog

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

I can't explain the remainder of the clue.

Can you help me to learn more?

(Other definitions for flog that I've seen before include "Hit - sell" , "Exchange for money" , "-- Hitler" , "Beat with a whip or rod" , "Lash" .)

I've seen this clue in the Evening Standard.

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