That can be fixed without replacing the whole nut. If it's bone, you can fill it with bone dust and CA. If you don't have any bone dust, or if it's plastic, use baking soda and CA. Let it harden 24 hours and re-cut the slot.
There are lots of YT videos on how to do this.

It's not always the best remedy, but it works and I've seen more experienced repairers/luthiers than I use it.
I have a couple of guitars where I did this (at least 5 years ago) and have not had any problem.