Writer's blood given to daughter in small bottle (4,5)
I believe the answer is:
gore vidal
'writer's' is the definition.
(US writer and intellectual)
'blood given to daughter in small bottle' is the wordplay.
'blood' becomes 'gore' (synonyms).
'given to' says to put letters next to each other.
'daughter' becomes 'd'.
'in' indicates putting letters inside.
'small bottle' becomes 'vial' (I've seen this before).
'd' put within 'vial' is 'vidal'.
'gore'+'vidal'='GORE VIDAL'
(Other definitions for gore vidal that I've seen before include "he writes" , "American novelist and playwright, b. 1925" .)