One getting up part of staircase (5)
I believe the answer is:
riser
I believe this is a double definition.
'one getting up' is the first definition.
(one rising or getting up)
'part of staircase' is the second definition.
(vertical support between staircase steps)
(Other definitions for riser that I've seen before include "Vertical piece between two stair treads" , "Vertical piece between treads of staircase" , "One who has stopped sleeping" , "Pipe for upward flow" , "upright portion of step" .)