Leading climber has breather on summit (5)
I believe the answer is:
crest
'summit' is the definition.
('crest' can be a synonym of 'summit')
'leading climber has breather' is the wordplay.
'leading' says to take the initial letters.
'has' says to put letters next to each other.
'breather' becomes 'rest' (I've seen this before**).
The initial letter of 'climber' is 'c'.
'c'+'rest'='CREST'
'on' is the link.
(Other definitions for crest that I've seen before include "Top point of hill or wave" , "Head" , "top position" , "Plume on a helmet" , "Badge" .)