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We have existing borders in Openstreetmap and borders which were converted from a shape file we want to import.
Getting started takes some discovery of what is already there.
Downloading the missing parts of the national borders of the neighbouring countries to the North and the East
First, selecting the existing boundary ways on the map, then selecting the parent relations in the properties pane
Then right mouse button; 'Download incomplete members'
The existing ways have many tags
The ways converted from the shapefiles only have boundary=administrative.
We will need to split in that corner. That one is easy
p splits a way in JOSM
Select a segment of the existing boundary pressing 3 zooms to selection
Zoom in to the other end of that segment.
And download more data along the border
It is not clear to me why the border was split there. There are no other borders joining at that point.
Looking around a bit.
Split our new border way here too
If we split here, we'll have an existing and a new border which correspond.
So we can apply the geometry of the border we want to import, to the existing one
After selecting the existing way in zooming out to it, we can continue with the next segment
Our imported boundary needs to be split where a lower level boundary joins.
We want to merge the boundary segments and then fix the lower level boundary.
They still need to be split where other borders join them.