Patrol
Patrol the sector and eliminate any Syndicate forces with extreme prejudice, then return back to Outpost 45. At least, that's how it's supposed to go.
Welcome to the 'default' overmap gamemode for NSV13 which tasks you and the rest of the crew with committing a varying amount of interstellar warfare against the Syndicate. This mode requires 10 Players to have a chance of rolling. You can check your objectives and their completion status at any time using a communications console. This also has the knock-on effect of immediately checking if they've been completed and, if they have, offering you a ride home.
Tickets
Patrol rounds assign you, the crew, a requirement to collect a set number of Tickets for NT. (Usually 1000 tickets)
Tickets are earned by defeating hostile fleets in combat, with higher risk and more dangerous fleets offering more, whilst weaker fleets offer less. Alternatively, Tickets can be earned by completing missions granted to you by trade stations, these also come with rewards of their own on as well as tickets.