Egghead meets up with respect (6)
I believe the answer is:
esteem
'respect' is the definition.
(I know that respect can be written as esteem)
'egghead meets up' is the wordplay.
'egghead' becomes 'e' (head letter of 'egg').
'up' says the letters should be written backwards (in down clue: letters go upwards).
'meets' back-to-front is 'steem'.
'e'+'steem'='ESTEEM'
'with' is the link.
(Other definitions for esteem that I've seen before include "Revere(nce)" , "Think highly of, have regard for" , "Honour - regard" , "judge" , "Respect, admire" .)