The most common and most likely answer to this crossword clue is the 9 letter word TENACIOUS
I've seen this crossword clue in The Daily Telegraph
T
E
N
A
C
I
O
U
S
More clues leading to the result TENACIOUS
- Determined action – sue for reconstruction
- Use action mistaken as firm
- Tough to abandon EU, so I can’t
- Determined airman, one in number over America
- Dogged by extremely unspeakable actions following representation
- Persistent, and flying out in case
- Firm can set out to restrict debt
- Firm surprised by debts?
- Firm that’s into sauce-manufacturing
- Perhaps use caution — departing unionist is stubborn
Buddy explains!

The straight part
We know that "Persistent" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case persistent = tenacious.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does TENACIOUS mean?
TENACIOUS adjective- Clinging to an object or surface; adhesive.
- Unwilling to yield or give up; dogged.
- Holding together; cohesive.
- Having a good memory; retentive.