Soak for a high price (5)

I believe the answer is:

steep

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'soak' is the definition.
(steeping is a kind of soaking)

I cannot understand how the rest of the clue works.

(Other definitions for steep that I've seen before include "Soak; expensive (price)" , "Soak thoroughly - precipitous" , "Having a sharp incline" , "Difficult" , "Stiff - thoroughly wet" .)

I've seen this clue in the Evening Standard.

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