Stubborn, he died earlier than expected crossing desert (8)
I believe the answer is:
obdurate
'stubborn' is the definition.
(obdurate means stubborn or obstinate)
'he died earlier than expected crossing desert' is the wordplay.
'he died' becomes 'ob' ('ob.' can mean 'died' from the Latin obiit).
'earlier than expected' becomes 'due' (I can't justify this - if you can you should give a lot more credence to this answer).
'crossing' is an insertion indicator.
'desert' becomes 'rat' (abandon treacherously).
'due' placed around 'rat' is 'durate'.
'ob'+'durate'='OBDURATE'
Can you help me to learn more?
(Other definitions for obdurate that I've seen before include "hard to influence" , "Unyielding - cruel" , "Not to be persuaded" , "Stubborn and unyielding" , "Impervious to persuasion" .)