The most common and most likely answer to this crossword clue is the 9 letter word PERSEVERE
I've seen this crossword clue in The Times
P
E
R
S
E
V
E
R
E
More clues leading to the result PERSEVERE
- A Spartan is to display determination
- Continue to be harsh on sal
- To keep going is hard after benefit cut
- To keep going is difficult after exercises, right?
- Go on about trailing first lady's representative around
- Continue in the face of difficulty, for every Spartan
- Carry on to each extreme
- Exercises Rex finds demanding? Struggle on!
- Soldier on a grave
- Remain by ascetic
Buddy explains!

The straight part
We know that "to display determination" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case to display determination = persevere.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 PERSEVERE mean?
PERSEVERE verb- To persist steadfastly in pursuit of an undertaking, task, journey, or goal, even if hindered by distraction, difficulty, obstacles, or discouragement.
- To stay constant; to continue in a certain state; to remain.