First woman to pause where there's a stiff climb (7)
I believe the answer is:
everest
'where there's a stiff climb' is the definition.
'first woman to pause' is the wordplay.
'first woman' becomes 'eve' (I've seen this before).
'to pause' becomes 'rest' (rest is a kind of pause).
'eve'+'rest'='EVEREST'
(Other definitions for everest that I've seen before include "Mountain named after a British surveyor general of India" , "High mountain" , "Highest peak" , "One conquered in 1953" , "Mountain on the Nepal-Tibet border" .)