Start of Lennon's Imagine reworked, conveying modern message (8)
I believe the answer is:
emailing
'conveying modern message' is the definition.
(modern communication method)
'start of lennon's imagine reworked' is the wordplay.
'start of' suggests taking the first letters.
'reworked' is an anagram indicator.
The initial letter of 'lennon' is 'l'.
'l'+'imagine'='limagine'
'limagine' is an anagram of 'EMAILING'.
(Other definitions for emailing that I've seen before include "correspondence?" , "Sending messages" , "Communicating electronically" .)