I am playing though the necron campaign and have 3 active fleets but I have a capacity for 7. Do I unlock more fleets as I play though the campaign or can I start new fleets through some part of the UI that I am missing?
You can get more fleets. When you're on a friendly system with empty fleet slots on the left, hovering over them will show a "+" sign. Click it, and it'll present a new Hero (Who commands the new fleet) to hire.