Determination that could decide who succeeds (4)
I believe the answer is:
will
This might be a double definition.
'determination that' is the first definition.
'will' can be an answer for 'determination' (will can mean determination or desire). I'm not sure about the rest of the definition.
'decide who succeeds' is the second definition.
'will' can be an answer for 'decide' (thesaurus). I'm not certain of the rest of the definition.
'could' is the link.
Can you help me to learn more?
(Other definitions for will that I've seen before include "Final disposition" , "mind" , "self-control" , "Written directions for disposal of estate after death" , "Record of final wishes and testament" .)