If you zoom in further you will notice that the area is well mapped. A different amount of detail is rendered on the tiles at different zoom levels.
If you have detailed plans for roadworks you would likely need explicit permission from the copyright holders for use in OSM and comply with the import guidelines.
See https://wiki.openstreetmap.org/wiki/Import/Guidelines
Then you would need to process the plans into a form to add the OSM, including using the correct projection coordinate system. If using an image you would need to warp/georeference to match osm.
There are many varied way of processing data into a form suitable for osm and I will leave that for you to investigate as it can be very complex and time consuming and if not done correctly with help from local mappers can be a disaster to rectify. Proceed cautiously.
https://wiki.openstreetmap.org/wiki/Import/Software
If already in a form that JOSM can open you could merge sections that are suitable for OSM and tag with usual tags used in OSM or you could use the plans as a background and draw the roads (edit) in to the OSM directly.
After getting this far through my reply I think you will agree that this small area you are wanting to update is more easily accomplished by doing more simply using one of the main editors like iD, JOSM or the new Potlatch 3 when released and using the aerial imagery and gps traces that are available. You can also use a gps receiver and camera to walk/ride/drive the new streets and add to the editor if they are not yet on imagery.
https://learnosm.org/en/
