Send out letter from Athens with name from the East (7)
I believe the answer is:
emanate
'send out' is the definition.
(I've seen this before)
'letter from athens with name from the east' is the wordplay.
'letter from athens' becomes 'eta' (letter of the Greek alphabet).
'with' is a charade indicator (letters next to each other).
'from the east' shows that the letters should be reversed in order (on a map from right to left).
'eta'+'name'='etaname'
'etaname' in reverse letter order is 'EMANATE'.
(Other definitions for emanate that I've seen before include "Rise" , "Come out (of source)" , "spring" , "Issue forth, from a source" , "Issue or originate from manatee" .)