President covers up extremely important case (8)
I believe the answer is:
ablative
'case' is the definition.
(ablative is a kind of case)
'president covers up extremely important' is the wordplay.
'president' becomes 'abe' (Abraham (Abe) Lincoln).
'covers' is an insertion indicator.
'up' is a reversal indicator (in down clue: letters go upwards).
'extremely important' becomes 'vital' (I've seen this before).
'vital' in reverse letter order is 'lativ'.
'abe' going around 'lativ' is 'ABLATIVE'.
(Other definitions for ablative that I've seen before include "A case in grammar" , "Case in Latin denoting 'by' or 'with' the associated noun" .)