Mapping Center Answer:

Firstly, you could use the Reshaping Representations tool in the Production Mapping toolset though, of course, this does require you to have these tools.

Unfortunately, without access to these tools there is no easy Cartographic Representations solution to this situation in ArcMap since there are a large number of vertices in the original (green) line. You could edit the original feature using the Editing tools though, of course, this will modify the geometry of the original feature and not the Representation. Alternatively, you could select and delete a large number of the vertices in the Representation and then use the remaining vertices to align with the new boundary.