How to network and not to get fired?

I’m working FT and want to lateral to IB. I understand I need to network, but I am not sure how to do it as a working professional. As a student, the situation is very clear for me – I was studying, didn't work FT so weren't tied to any employer and could openly say I wanted a job at the given company.

However, the situation gets tricky when you have a few years of work experience and want to lateral. Of course an initial aim of any networking chat is to learn more about a bank and a specific team, but then should I openly express my interest in joining that team? Frankly speaking, I am afraid the person I would be networking with could let know my current employer, or even the team, that I’m trying to lateral and get an offer elsewhere. Eventually, I don’t want to get fired without anything lined up just because someone I networked with couldn’t be discreet for whatever reason. Before you tell me it’s normal for employees to just keep an eye open for new career opportunities, let me tell you that my company has a weird culture (e.g. bashing employees, who decided to resign, in internal communications) and I’m pretty sure that lateralling to IB would be seen a kind of betrayal.

This said, please enlighten me how to network as a working professional and not to get fired. To what extent I should express my interest in moving to the given bank/team assuming I want to do so?

I don't have much experience in networking and I need some advice. Thanks!