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Have obligation to take on credit for shrink (5)

Ross

I believe the answer is:

cower

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'for shrink' is the definition.
(shrink can mean to cower from something)

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for cower that I've seen before include "Shrink back in fear" , "Show abject fear" , "Cringe, crouch" , "Cringe in fear" , "to emulate Burns's wee beastie" .)

I've seen this clue in The Irish Times.
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