Transmit again about unfinished letter (5)
I believe the answer is:
rerun
'transmit' is the definition.
(rerunning is a kind of transmiting)
'again about unfinished letter' is the wordplay.
'again' becomes 're' (prefix meaning 'again').
'about unfinished letter' becomes 'run' (I can't justify this - if you can you should believe this answer much more).
're'+'run'='RERUN'
Can you help me to learn more?
(Other definitions for rerun that I've seen before include "Show again on TV" , "Repeated programme" , "Another airing" , "Show or perform again" , "Second broadcast" .)