Perhaps use caution — departing unionist is stubborn (9)
I believe the answer is:
'stubborn' is the definition.
(similar in meaning)
I can't explain the remainder of the clue.
Can you help me to learn more?
(Other definitions for tenacious that I've seen before include "refusing to give up", "Persevering", "Holding fast", "Holding or sticking firmly", "Persistent in holding on".)