The height of distinction (8)
I believe the answer is:
eminence
I believe this is a double definition.
'the 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?" , "Esteem" , "Important person" , "High status importance" , "Bank" .)