Meets up with an egghead to honour (6)
I believe the answer is:
esteem
'honour' is the definition.
(esteem is a kind of honour)
'meets up with an egghead' is the wordplay.
'up with' indicates anagramming the letters.
'an egghead' becomes 'e' (head letter of 'egg').
'meets' anagrammed with 'e' can make 'ESTEEM'.
'to' is the link.
(Other definitions for esteem that I've seen before include "High regard as for customer" , "'Regard, respect (6)'" , "Honour - regard" , "credit" , "judge" .)