Start to work on his claim that's disputed and fanciful (9)
I believe the answer is:
whimsical
'fanciful' is the definition.
(I've seen this before)
'start to work on his claim that's disputed' is the wordplay.
'start to' says to take the initial letters.
'on' is a charade indicator (letters next to each other).
'that's disputed' is an anagram indicator.
The first letter of 'work' is 'w'.
'his'+'claim'='hisclaim'
'hisclaim' anagrammed gives 'himsical'.
'w'+'himsical'='WHIMSICAL'
'and' is the link.
(Other definitions for whimsical that I've seen before include "Playfully quaint" , "Fanciful, fantastical" , "Capricious" , "Quirky" , "Playfully fanciful" .)