Hospital overlooks number for summit (6)
I believe the answer is:
height
'summit' is the definition.
('height' can be a synonym of 'summit')
'hospital overlooks number' is the wordplay.
'hospital' becomes 'h'.
'overlooks' is a charade indicator (letters next to each other) (down clues only).
'number' becomes 'eight' (eight is a kind of number**).
'h'+'eight'='HEIGHT'
'for' acts as a link.
(Other definitions for height that I've seen before include "Dimension from top to bottom" , "Altitude or elevation" , "Loftiness" , "Rising ground; extreme example" , "summit" .)