Stop going up and down (4,2)
I believe the answer is:
pull up
'stop going' is the definition.
'pull up' can be an answer for 'stop' (to pull someone up is to stop them doing something). I'm not sure about the 'going' bit.
'up and down' is the wordplay.
'and' says to put letters next to each other.
'down' becomes 'pull' (synonyms).
'up' put after 'pull' is 'PULL-UP'.
(Other definitions for pull up that I've seen before include "Halt" , "Take to task" , "Exercise" , "park" , "Stop or cause to stop" .)