Statement in court case mostly taking care of Duke making impromptu comment (2-3)
I believe the answer is:
ad-lib
'impromptu comment' is the definition.
'statement in court case mostly taking care of duke' is the wordplay.
'statement in court case' becomes 'alibi'.
'mostly' means to remove the last letter.
'taking care of' is an insertion indicator.
'duke' becomes 'd'.
'alibi' with its final letter taken away is 'alib'.
'alib' enclosing 'd' is 'AD-LIB'.
'making' acts as a link.
(Other definitions for ad-lib that I've seen before include "Improvised remark" , "freely" , "Talk without notes" , "Extemporise" , "Depart from the text" .)