Chances are ultimately plentiful, for new arrival at the periphery (8)
I believe the answer is:
probably
'chances are' is the definition.
('chances are...' means 'probably')
'ultimately plentiful for new arrival at the periphery' is the wordplay.
I cannot quite see how this works, but
'for' could be 'pro' (as in being 'pro' something) and 'pro' is found within the answer.
This may be the basis of the clue (or it may be nonsense).
Can you help me to learn more?
(Other definitions for probably that I've seen before include "Almost certainly" , "Most possibly" , "In all likelihood" , "Likely" , "I expect so" .)