Height of distinction? (8)
I believe the answer is:
eminence
This clue is a double definition.
'height' is the first definition.
(thesaurus)
'distinction?' is the second definition.
('eminence' can be a synonym of 'distinction')
'of' is the link.
(Other definitions for eminence that I've seen before include "nobility?" , "Distinguished person" , "Acknowledged superiority in a particular sphere" , "Bank" , "Important person" .)