The most common and most likely answer to this crossword clue is the 10 letter word HEADSTRONG
I've seen this crossword clue in The Daily Telegraph
H
E
A
D
S
T
R
O
N
G
More clues leading to the result HEADSTRONG
- Wilful crime reported on main road
- Wilful leader’s weight about right? Good
- Stubborn leader, powerful
- Get hard with son terribly self- willed
- Showing wilfulness the gods ran amok
- Powerful teacher first is obstinate
- Obstinately determined the dragons must be beaten
- Refractory’s hot and danger’s spreading
- Stubborn alcoholic supports top on beer
- Leader, forceful and obstinately self-willed
Buddy explains!

The straight part
We know that "Obstinately determined" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case obstinately determined = headstrong.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 HEADSTRONG mean?
HEADSTRONG adjective- Determined to do as one pleases, and not as others want.