Staggering time for learner in draw (7)
I believe the answer is:
tottery
'staggering' is the definition.
(tottery means unsteady)
I don't understand the rest of the clue.
(Other definitions for tottery that I've seen before include "rocking" , "Unstable on one's feet" , "Frail" , "Moving insecurely" , "Likely to rock" .)