Letters announcing successor is a man (7)
I believe the answer is:
airmail
'letters' is the definition.
(airmail letter is a kind of letter)
'announcing successor is a man' is the wordplay.
'announcing' shows a homophone (sound like).
'successor' becomes 'heir' (synonyms).
'is a man' becomes 'mail' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'heir' sounds like 'air'.
'air'+'mail'='AIRMAIL'
Can you help me to learn more?
(Other definitions for airmail that I've seen before include "Way of communicating" , "Postal service" , "Flying post?" , "Letter delivery system" , "Speedy deliveries" .)