Finally doesn't finish a book (5)
I believe the answer is:
atlas
'a book' is the definition.
(I know that atlas is a type of book of facts)
'finally doesn't finish' is the wordplay.
'finally' becomes 'at last' (synonyms).
'doesn't finish' means to remove the last letter.
'atlast' with its final letter removed is 'ATLAS'.
(Other definitions for atlas that I've seen before include "One greatly burdened" , "Titan who supported the heavens" , "Titan compelled by Zeus to support the sky" , "Sort of book" , "Asian satin" .)