Write someone else’s book? That’s the spirit (5)
I believe the answer is:
ghost
This clue is a double definition.
'write someone else's book?' is the first definition.
(as in ghost-writing)
'the spirit' is the second definition.
(ghost is a kind of spirit)
'that's' is the link.
(Other definitions for ghost that I've seen before include "Spirit of the dead" , "who has a haunting act?" , "A spirit from the beyond" , "someone without much presence" , "Hamlet's spectral father" .)