Uneasy son a cutie dogged (9)
I believe the answer is:
tenacious
'dogged' is the definition.
(synonyms)
'uneasy son a cutie' is the wordplay.
'uneasy' is an anagram indicator.
'son'+'a'+'cutie'='sonacutie'
'sonacutie' with letters rearranged gives 'TENACIOUS'.
(Other definitions for tenacious that I've seen before include "Persevering" , "Persistent in holding on" , "Keeping a firm hold" , "Dogged" , "refusing to give up" .)