Agree to exchange letters (10)
I believe the answer is:
correspond
I believe this clue is a double definition.
'agree' is the first definition.
(I've seen this before)
'exchange letters' is the second definition.
(thesaurus)
'to' acts as a link.
(Other definitions for correspond that I've seen before include "Communicate; agree" , "answer" , "Keep in touch by letter" , "Swap letters" , "email, say?" .)