No heart for precipitous measure (4)

I believe the answer is:

step

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'measure' is the definition.
(I know that measure can be written as step)

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Other definitions for step that I've seen before include "Put foot on a pest" , "A pace for pets" , "bit of a dance" , "little walk?" , "Dance move" .)

I've seen this clue in The Times.

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