In my bathroom, I have an old fashion vanity light that operates with a pull chain. I want to update the light fixture but do not want to do major behind the wall construction since house is not mine. Is there a way to add a on-off switch to the backplate of the updated vanity light fixtures? The only ones I've been able to find are the same old style I have now. Thank you.

If you do not own the house, you should not do the work. Most local electrical inspectors require the owner, contractor or electrician file for the permit.

Changing the fixture is not all you have to do. You need to put in a switch loop and switch to control the new fixture.