Greatest height or peak (6)
I believe the answer is:
zenith
I believe this is a double definition.
'greatest height' is the first definition.
(I've seen this before)
'peak' is the second definition.
(I've seen this in another clue)
(Other definitions for zenith that I've seen before include "Point directly above the nadir" , "Peak" , "It's directly opposite to the nadir" , "The highest point directly above" , "The highest point overhead" .)