Father and Son: son goes off to be an author (5)
I believe the answer is:
gosse
'father and son' is the definition.
(I've seen this before)
'be an author' is the wordplay.
'be' becomes 'go' (going is a kind of being).
'an author' becomes 'sse' (I can't explain this - if you can you should give a lot more credence to this answer).
'go'+'sse'='GOSSE'
'son goes off to' is the link.
This may not be correct. Some or all of it may be part of another bit of the clue.
(Other definitions for gosse that I've seen before include "Sir Edmund --, British poet and critic" , "Father and son" .)