Insistent, resolute (7)
I believe the answer is:
adamant
I believe this is a double definition.
'insistent' is the first definition.
(I've seen this before)
'resolute' is the second definition.
(both can mean determined)
(Other definitions for adamant that I've seen before include "Determined and unyielding to requests" , "Hard and unrelenting" , "Fabulous rock" , "6a [PRINCESS IDA] 's fortress < for unyielding" , "Legendary rock" .)