moreover ArcGIS editor tools you can get help from Snap Tool, it would be very useful if new boundary is in polyline and old boundary is in polygon, your case is similar to case 3 in below images
Based on ArcGIS help manual:
The Snap Environment parameter allows for the vertices of the input features to be snapped to the vertices, edges, and end points of multiple layers or feature classes. When multiple snapping rules are given, they are prioritized as follows: from top to bottom in the tool dialog or from left to right in scripting.
The input features' vertices will be snapped to the nearest vertex, edge, or end point within the specified distance.
In the Snap Environment parameter, multiple snap rules can be designated using the same layer or feature class with a different type (END | VERTEX | EDGE).
If a layer or feature class with a selection is used as the input, only vertices of the selected features will be snapped.
When snapping features in one feature class to features in the same feature class, the feature with the lower Object or Feature ID will usually be snapped to the feature with the higher Object ID. For example, if points OBJECTID 1 and OBJECTID 2 are within the snapping distance, the point with OBJECTID 1 will be snapped to the location of the point with OBJECTID 2 (and not vice versa). Use the Sort tool to rearrange features so this snapping behavior can be controlled.
When the tool is used in ArcMap, the Snap Environment of the application is defaulted into the Snap Environment parameter, where it can be modified if desired.