The one that didn't get on with you (4)
I believe the answer is:
thee
'you' is the definition.
(historical second person pronoun)
'the one that didn't get on' is the wordplay.
I cannot quite understand how this works, but
'the' could be 't' (the is pronounced as a 't' sound in some dialects) and 't' is found within the answer.
The remaining letters 'hee' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'with' is the link.
Can you help me to learn more?
(Other definitions for thee that I've seen before include "Quaker 'you'" , "Archaic form of 'you'" , "Poetically you" , "You in the olden days" , "You (arch.)" .)