Thriller writer about to fill in family connection (6)
I believe the answer is:
greene
'thriller writer' is the definition.
'greene' can be an answer for 'writer' (novelist Graham Greene). I'm not sure about the 'thriller' bit.
'about to fill in family connection' is the wordplay.
'about' becomes 're' ('re' means regarding or about).
'to fill in' indicates putting letters inside.
'family connection' becomes 'gene' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
're' placed within 'gene' is 'GREENE'.
Can you help me to learn more?
(Other definitions for greene that I've seen before include "writer" , "Graham --, Eng. author" , "See 13" , "Graham -, English author (Brighton Rock)" , "Graham -, English novelist" .)