Communication by letter to Lima, possibly (1-4)
I believe the answer is:
'communication' is the definition.
(I've seen this before)
'letter to lima possibly' is the wordplay.
'letter' becomes 'e'.
'possibly' is an anagram indicator.
'lima' anagrammed gives 'mail'.
'e'+'mail'='E-MAIL'
'by' is the link.
(Other definitions for e-mail that I've seen before include "Web post" , "Electronic missive" , "Modern method of communication via Internet" , "Online post" , "Transmission of correspondence via internet" .)