The most common and most likely answer to this crossword clue is the 11 letter word PERSISTENCE
I've seen this crossword clue in The Daily Telegraph
P
E
R
S
I
S
T
E
N
C
E
More clues leading to the result PERSISTENCE
Buddy explains!

The straight part
We know that "determination" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case determination = persistence.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 PERSISTENCE mean?
PERSISTENCE noun- The property of being persistent.
- Of data, the property of continuing to exist after the termination of the program.
- Continuation of the previous day's weather (particularly temperature and precipitation statistics).