Replacing a section of wallpaper

First thing, I'm assuming you have wallpaper that's been saved to do the repair with and that you've looked at it vs the existing and it matches. The big problem here is that wallpaper ages and the old and new may not match well enough.

If it matches, I'd use a steamer to loosen the section. Then I'd let it mostly dry. Then cut a section of the new that an inch or so longer than the bad section. Lay it over the old, secure it with some tape, then use a razor and straightedge to cut through both new and old at the same time. Then remove the cut off section of the old and the new piece will mate with the cut off ends of the old. I would do this across a full width, do two widths if necessary, instead of having a vertical cut instead of a normal seam.