Rejected story covering degree communication (5)
I believe the answer is:
'communication' is the definition.
(email is a kind of communication)
'rejected story covering degree' is the wordplay.
'rejected' is a reversal indicator.
'story' becomes 'lie' (I've seen this before).
'covering' indicates putting letters inside.
'degree' becomes 'am' (AM is an example**).
'lie' enclosing 'am' is 'liame'.
'liame' reversed gives 'EMAIL'.
(Other definitions for email that I've seen before include "Send one online" , "Internet-borne communication" , "Post" , "Message sent via computer" , "Messages between computer terminals" .)