Labour target regenerating after cuts at the top (5)

I believe the answer is:

hydra

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'labour target' is the definition.
The definition and answer can be both people as well as being singular nouns.
I also know that 'labour' relates to this answer.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for hydra that I've seen before include "M any-headed monster fought by Hercules" , "Stars" , "Proliferating-head monster" , "Small red-berried tree" , "Many-headed monster of Greek mythology" .)

I've seen this clue in The Independent.

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