Actor coached with one in test of speech (10)
I believe the answer is:
oratorical
'of speech' is the definition.
(oratory is public speaking)
'actor coached with one in test' is the wordplay.
'coached with' is an anagram indicator (I've seen 'coach' mean this (coach can mean to change or improve)).
'one' becomes 'i' (roman numeral).
'in' is an insertion indicator.
'test' becomes 'oral' (oral is a type of examination).
'actor' with its letters mixed up with 'i' gives 'torica'.
'torica' going within 'oral' is 'ORATORICAL'.
(Another definition for oratorical that I've seen is " Relating to public speaking".)