Local speech day: smart chap opens it (7)
I believe the answer is:
dialect
'local speech' is the definition.
(eg a regional dialect)
'day smart chap opens it' is the wordplay.
'day' becomes 'd' (abbreviation for day).
'smart chap' becomes 'alec' (as in the phrase 'smart Alec').
'opens' means one lot of letters goes inside another (insertion requires an opening to be made).
'alec' inserted within 'it' is 'ialect'.
'd'+'ialect'='DIALECT'
(Other definitions for dialect that I've seen before include "Regional form of speech" , "Local language variation" , "Vernacular" , "Material damage" , "Local language version" .)