Move to and fro, for example, around centre of Norwich (4)
I believe the answer is:
sway
'move to and fro' is the definition.
(I've seen this in another clue)
'for example around centre of norwich' is the wordplay.
'for example' becomes 'say' ('say' can be used to introduce an example).
'around' is an insertion indicator.
'centre of' means to look at the middle letters.
The centre of 'norwich' is 'w'.
'say' placed around 'w' is 'SWAY'.
(Other definitions for sway that I've seen before include "Vacillate" , "Lean from side to side - influence" , "Control" , "Swing - lean - persuade" , "Influence; dominance" .)