There will be an STP recalculation for all vlans that are common to the switches.
You can't prevent that and you should have an outage for this.
You should also enable STP on all switches because as you say you have a loop.
Not having STP enabled would be a very bad idea.
Make your existing switch the STP root for all vlans and if you want pick one of the others as secondary.
The root is more important.
You should use RSTP if available on all switches.
There are additional things like rootguard which could be enabled but if you want to keep it simple just enable STP and set the existing switch as root and that should work in your setup.
Do not bring up the ports without STP.
The outage should be short ie. with RSTP less than a minute but there will be a convergence because currently you don't have STP running anywhere.
Jon