Improvised, which compensated for (4,2)

I believe the answer is:

made up

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'compensated for' is the definition.
'made up' can be an answer for 'compensated' ('make up' can be a synonym of 'compensate'). I'm unsure of the 'for' bit.

I don't understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for made up that I've seen before include "painted" , "Supplied" , "Given slap" , "Chuffed" , "Put together" .)

I've seen this clue in the Evening Standard.

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