Modify piece of local terminology (5)
I believe the answer is:
alter
'modify' is the definition.
(thesaurus)
'of local terminology' is the wordplay.
'of' indicates a hidden word.
'ALTER' is hidden within 'local terminology'.
'piece' is the link.
(Other definitions for alter that I've seen before include "Change, make different" , "Revise" , "reform" , "Alert to change" , "shift" .)