If the existing light is still functional and the seal around it is intact, I wouldn't remove it to install another plate holder like what just broke. You'll risk a leaking light and if one broke, chances are another similar one will do the same.
When mine died by cracking and falling off the trailer (fortunately at home so I didn't need a replacement license plate) I took that opportunity to install LED tail/brake lights and a "PERMANENT" plate holder. This is the one I used, it has 4 screws to mount the holder to the trailer and then 2 screws to mount the plate to the holder.
I applied butyl putty tape across the entire back, positioned it on the trailer, then used 4 self tapping screws to hold it in place. After tightening the screws, I used a plastic razor blade to trim the excess butyl putty from the edges and sealed the screwheads with some left over DICOR putty from doing my roof.
Here's a photo and a link for what I used. If you mount it under that tail light, you won't need an extra plate light:
https://www.amazon.com/Kaper-II-1M-V...76285822&psc=1