Propose that you subject yourself to (6)

I believe the answer is:

submit

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'propose' is the definition.
(submitting is a kind of proposing)

I cannot understand how the remainder of the clue works.

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(Other definitions for submit that I've seen before include "Hand in" , "Surrender or propose" , "Surrender, or present for decision" , "Put forward for approval or yield" , "Defer to the will of another" .)

I've seen this clue in the Evening Standard.

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