Didn't include synonym for 'hand' in dictionary (7)
I believe the answer is:
omitted
'didn't include' is the definition.
(omit can mean to exclude)
'synonym for hand in dictionary' is the wordplay.
'synonym for hand' becomes 'mitt' (mitt can informally mean someone's hand).
'in' is an insertion indicator.
'dictionary' becomes 'OED' (Oxford English Dictionary).
'mitt' put within 'oed' is 'OMITTED'.
(Other definitions for omitted that I've seen before include "Failed" , "not mentioned" , "Left out - neglected" , "Excluded" , "Hairdressing" .)