Stubborn stain to be specially treated (9)
I believe the answer is:
obstinate
'stubborn' is the definition.
('obstinate' can be a synonym of 'stubborn')
'stain to be specially treated' is the wordplay.
'specially treated' indicates an anagram (I've seen this in other clues).
'stain'+'to'+'be'='staintobe'
'staintobe' is an anagram of 'OBSTINATE'.
(Other definitions for obstinate that I've seen before include "Cussed" , "Female bird" , "Inflexible" , "Like mules" , "Stubbornly persistent" .)