Losing head, trample marsh plant (4)

I believe the answer is:

rush

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'marsh plant' is the definition.
(I know that rush is a type of marsh plant)

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for rush that I've seen before include "Reed" , "Spate" , "Drug-induced euphoria" , "Hurry to the grassy plant" , "Be too hasty or too fast" .)

I've seen this clue in The Times.

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