Going both ways don't, for a change (2,3,3)
I believe the answer is:
to and fro
'going both ways' is the definition.
Both the answer and definition are adverbs. Maybe there's a link between them I don't understand?
'don't for a change' is the wordplay.
'change' indicates an anagram.
'dont'+'for'+'a'='dontfora'
'dontfora' with letters rearranged gives 'TO-AND-FRO'.
Can you help me to learn more?
(Other definitions for to and fro that I've seen before include "both ways" , "This way and that, back and forth" , "Backwards and forwards" , "Shuttle's motion" , "Back and forth like pendulum (2.3.3)" .)