Use 'in that event' to talk about backup plans or actions if an expected situation occurs. If our main speaker cancels, in that event, we'll need a substitute.
Pro Tip 2/3
Formal Tone
'In that event' is more formal and used in professional or serious contexts, unlike 'if that happens'. In that event, the committee will convene to make an alternative decision.
Pro Tip 3/3
Cause and Effect
Shows a cause-and-effect relationship, indicating what should be done after an event occurs. The weather may turn bad; in that event, the event will move indoors.