Exist with just a part interest (6)
I believe the answer is:
behalf
'a part interest' is the definition.
'behalf' can be an answer for 'interest' (behalf is a kind of interest). I'm not certain of the 'a part' bit.
'exist with just' is the wordplay.
'exist' becomes 'be' (synonyms).
'with just' becomes 'half' (I can't explain this - if you can you should believe this answer much more).
'be'+'half'='BEHALF'
Can you help me to learn more?
(Other definitions for behalf that I've seen before include "On - of means in someone's interest" , "Part - account" , "(Someone's) benefit or sake" , "Sake, interest, benefit" , "(A person's) interest" .)