The old man's upset by nuts
I believe the answer is:
almonds
'nuts' is the definition.
(I know this)
'the old man's upset' is the wordplay.
'upset' indicates an anagram.
'old'+'mans'='oldmans'
'oldmans' with letters rearranged gives 'ALMONDS'.
'by' is the link.
(Other definitions for almonds that I've seen before include "Sold man on kind of nuts" , "Man sold (anag.)" , "Fruits for marzipan" , "Nuts used to make marzipan" .)