The most common and most likely answer to this crossword clue is the 8 letter word TENACITY
I've seen this crossword clue in The Daily Telegraph
T
E
N
A
C
I
T
Y
More clues leading to the result TENACITY
- In Vietnamese festival I can rise, having Yankee's perseverance
- Eccentric in act, yet to show persistence
- Figure a place like Damascus shows resolve
- Doggedness shown by number one team from Manchester
- After tax rises American banking centre showing resolve
- Resolve shown in large town after Etna’s eruption
- determination
- Resolve mainly intact, yet must be broken
- Determination of town on Etna destroyed
- Determination shown by ‘X’, a population centre
Buddy explains!

The straight part
We know that "firmness of purpose" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case firmness of purpose = tenacity.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 TENACITY mean?
TENACITY noun- The quality or state of being tenacious, or persistence of purpose; tenaciousness.
- The quality of bodies which keeps them from parting without considerable force, as distinguished from brittleness, fragility, mobility, etc.
- The effect of this attraction, cohesiveness.
- The quality of bodies which makes them adhere to other bodies; adhesiveness, viscosity.
- The greatest longitudinal stress a substance can bear without tearing asunder, usually expressed with reference to a unit area of the cross section of the substance, as the number of pounds per square inch, or kilograms per square centimeter, necessary to produce rupture.