The most common and most likely answer to this crossword clue is the 4 plus 4 letter word FREE WILL
I've seen this crossword clue in The Daily Telegraph
F
R
E
E
W
I
L
L
More clues leading to the result FREE WILL
- We'll fire haphazardly, showing ability to make decisions
- Film of an orcawas spontaneous
- Legal document not charged for offers autonomy
- Self-determination a service offered by generous solicitors?
- The ability to choose to skip the end of a film about a whale
- Volition‘s something that may get Spooner a little ruffled?
- Emancipate wife? Detrimental to give independence!
Buddy explains!

The straight part
We know that "Self-determination" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case self-determination = free will.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.