Praise work I abandoned, taken on by former partner (5)

I believe the answer is:

extol

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'praise' is the definition.
(extolling is a kind of praising)

I can't explain the remainder of the clue.

(Other definitions for extol that I've seen before include "be lavish with praise" , "Acclaim" , "Speak highly" , "Warmly approve of" , "Cry up" .)

I've seen this clue in The Independent.

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