Dogged, tenacious (10)
I believe the answer is:
persistent
I believe this clue is a double definition.
'dogged' is the first definition.
(I know that dogged can be written as persistent)
'tenacious' is the second definition.
(I know that tenacious can be written as persistent)
(Other definitions for persistent that I've seen before include "not giving up" , "Determined" , "Tenacious; constant" , "Endless" , "single-minded" .)