Still a bit bright-eyed after rising (3)
I believe the answer is:
yet
'still' is the definition.
(yet can mean still or so far)
'a bit bright-eyed after rising' is the wordplay.
'a bit' indicates the answer is hidden within the clue (I've seen 'bit of' mean this).
'rising' is a reversal indicator (in a down clue, letters go up).
'tey' is hidden within 'bright eyed after'.
'tey' reversed gives 'YET'.
(Other definitions for yet that I've seen before include "Still; nevertheless" , "Up to the present time" , "Up to this time and continuing" , "Though; still" , "Still; however" .)