Frank's love for a writer (4)
I believe the answer is:
open
'frank's' is the definition.
(synonyms)
'love for a writer' is the wordplay.
'love' becomes 'o' (love means zero in tennis).
'for' is a charade indicator (letters next to each other).
'a writer' becomes 'pen' (something which writes).
'o'+'pen'='OPEN'
(Other definitions for open that I've seen before include "Not closed; set going" , "Unrestricted; ready for business" , "Admitting customers" , "Undecided" , "Frank; unfold" .)