Happen to come across sum left for old teacher (9)
I believe the answer is:
aristotle
'teacher' is the definition.
(I have seen 'Peripatetic teacher' mean 'aristotle' so perhaps 'teacher' could also mean 'aristotle')
'happen to come across sum left for old' is the wordplay.
'happen' becomes 'arise' (arising is a kind of happening).
'to come across' means one lot of letters goes inside another.
'sum' becomes 'tot' ('tot' can be a synonym of 'sum').
'left for old' becomes 'l' (I can't explain this - if you can you should believe this answer much more).
'tot'+'l'='totl'
'arise' placed around 'totl' is 'ARISTOTLE'.
Can you help me to learn more?
(Other definitions for aristotle that I've seen before include "Greek philosopher (Poetics, Politics)" , "Philosopher - treats oil (anag)" , "Thinking Greek" , "Ancient Athenian philosopher, pupil of Plato" , "noted thinker" .)