Lear production upset part of Hamlet (7)
I believe the answer is:
laertes
'part of hamlet' is the definition.
(Laertes is a role in Hamlet)
'lear production upset' is the wordplay.
'production' is an anagram indicator.
'upset' becomes 'tes' (I've seen this in other clues).
'lear' with letters rearranged gives 'laer'.
'laer'+'tes'='LAERTES'
(Other definitions for laertes that I've seen before include "Ophelia's brother (Shak.)" , "... killer of prince" , "Brother of Ophelia (Hamlet)" , "Man responsible for Ulysses" , "character in Hamlet" .)