Telegraph initially published writer's copy (10)
I believe the answer is:
transcribe
'copy' is the definition.
(I've seen this before)
'telegraph initially published writer's' is the wordplay.
'initially' indicates taking the first letters.
'published' becomes 'ran' (running is a kind of publishing).
'writer' becomes 'scribe' (scribe is a kind of writer**).
The first letter of 'telegraph' is 't'.
't'+'ran'+'scribe'='TRANSCRIBE'
(Other definitions for transcribe that I've seen before include "Copy into another form" , "Take down" , "Copy out longhand" , "write up" .)