If you use a system which integrates with Amazon echo, you may be able to use that as a “man in the middle” where your security system sensor triggers an Alexa routine (not a smart things routine) which turns on a virtual switch in smartthings, and then you can have that switch coming on trigger pretty much any smartthings activity you want.
This works quite well and lots of people are using it, but it is a cloud to cloud integration which may not be what you want.
There isn’t anything in the US which directly replaces the former ADT/smartthings dual logo system at this time.
The other alternative is to switch hubs. Abode is a nice system with better security features than smartthings has and decent home automation integration. It also has a Pretty good app and much better video integration. Normally you would use that instead of smartthings but if you did want to use both, or you can use Ifttt for some limited integration.
Ring is a nice simple security system, very inexpensive, but again integration with SmartThings would be through Echo or through Ifttt.
From ADT’s Point of view, their replacement for the smartthings/ADT system Is “blue by ADT“ (formerly called “lifeshield“) which has some home automation, although not as much as abode.
So it really depends on the exact details of what functionality you want to reproduce. there are lots of choices in this category (inexpensive DIY security with optional monitoring and some home automation features), but the exact offerings do differ.