A pie-filling supplier's in dispute (2,4)
I believe the answer is:
at odds
'in dispute' is the definition.
'a pie-filling supplier's' is the wordplay.
'pie' becomes 'patty' (patty is a kind of pie).
'filling' indicates the central letters (the letters which fill the word).
'supplier's' becomes 'odds' (I can't explain this - if you can you should give a lot more credence to this answer).
The middle of 'patty' is 't'.
'a'+'t'+'odds'='AT ODDS'
Can you help me to learn more?
(Other definitions for at odds that I've seen before include "At variance (with)" , "In opposition or disagreement" , "In conflict with, oppposed to (2,4)" , "In disagreement or dispute" , "Conflicting (with)" .)