Within one mile of the summit (4)
I believe the answer is:
acme
'the summit' is the definition.
('acme' can be a synonym of 'summit')
'within one mile' is the wordplay.
'within' indicates putting letters inside.
'one' becomes 'ace' ('ace' can be a synonym of 'one').
'mile' becomes 'm' (common abbreviation).
'ace' placed around 'm' is 'ACME'.
'of' is the link.
(Other definitions for acme that I've seen before include "Pinnacle" , "high peak" , "Highest level or degree attainable" , "crown" , "Height of achievement" .)