HI @steve.morey there is an approval process available if you use self-registration however if you grant the ability to create users to a PU, there is no way to put an approval process around this.
We setup a group that captures new users based on data added to a custom field and then we have a notification going out whenever a new user is added to the group. You could use that to get notified that a new user was created.
There is also a notification specific to new user creation however it hasn't worked for us...maybe you’ll have better luck. you can find these under the notifications app in the Users section; there are a few that might work for you.