Thankfully I haven't had to deal with a positive STI test.
Other health issues, but not STI, like latex sensitivity.
I'm rather very low volume. So I would contact the visits I've had since my last test to let them know just to get tested.
We practice safe encounters so the likelihood is low, but not non-existent. I might hurt my reputation, but I would prefer to let them know, than to hide my tracks, and risk the spread to colleagues, or other clients. Or risk of reinfection because the source wasn't alerted to the potential problem they are spreading.
I would hope honesty, and willingness to set reputation aside for the safty of those I see would matter more to them in the end. I'm trusting them not to give me something, like they are trusting me not to give them anything. Trust doesn't mean lack of protection, it means trusting the appropriate protection is used with others aswell as our encounters to reduce possible risks.