One getting up only a bit of the staircase (5)
I believe the answer is:
riser
I believe this is a double definition.
'one getting up' is the first definition.
(I've seen this before)
'only a bit of the staircase' is the second definition.
(Other definitions for riser that I've seen before include "Upwardly mobile type" , "Front of a step; vertical pipe" , "Section of flight" , "upright portion of step" , "He gets up" .)