Have more staying power than half-hearted social reject (7)
I believe the answer is:
outlast
'have' is the definition.
The answer and definition can be both to do with fundamental existence as well as being verbs in their base form.
Maybe you can see an association between them that I don't see?
'staying power than half-hearted social reject' is the wordplay.
I cannot quite see how this works, but
'half' could be 'last' (last half is a kind of half) and 'last' is found in the answer.
The remaining letters 'out' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...
'more' acts as a link.
Can you help me to learn more?
(Other definitions for outlast that I've seen before include "Go on longer than" , "Persist longer than" , "Survive beyond" , "carry on after all others" , "Endure beyond" .)