Here is an example of a Patron Encounter developed for the Traveller Sandbox Experiment. Ultimately, I'd suggest that you develop at least six of these to help create hooks that lead into your campaign setting. I'm probably only going to do two or three as examples, but these are fairly straightforward, and I think writing them up will help any Referee when inspiration is not striking on a particular evening.
With that in mind, I'm going to start with a patron encounter that emphasizes a sector-wide element, namely the Factor of Malsumis:
Jamie Engstrom, Starship Pilot
Required: Social Sciences, Sensors; Scientific Equipment
Reward: Cr3,000 per person, or a small percentage of any profits from the venture.
Jamie Engstrom is a pilot for hire. His most recent contract involved chartering his scout ship and his services to agents of the Factor of Malsumis, who performed a number of sensor scans of specific moons in a nearby system. As the Factor is known for her interest in Progenitor sites, Jamie ran his own scans of the various satellites, in hopes of discovering a previous unknown site and staking a claim on it. Sadly, he isn't sure what he should be looking for, and has hopes of hiring a skilled archeologist to help him interpret the data and then stake a claim on the site, should there be one. Jamie would prefer to offer a small percentage, definitely no more than 10%, in case this doesn't pan out. A skillful negotiator could talk him up to 20%, but anything above that and he'll walk.
Jamie Engstrom is in a race with the Factor's agents to return to any site that might have shown up on sensor scans. He's signed a non-disclosure contract, but feels confident that a good attorney could nullify it if there's an actual discovery. Jamie hasn't thought through all of the legal ramifications, and tends to be a "get rich quick" idealist. One of the sensor scan results look promising, and upon hearing the news, Jamie will want to quickly be underway, in order to check it out. In all of the options presented below, further development is left to the discretion of the Referee.
1. All is as it appears. The moon in question does appear to hold the remains of a Progenitor site that was utterly destroyed in an ancient battle. Nonetheless, it is an important discovery, and will bring in some money. The Factor's Agents arrive 1d6 days after the team gets there, which further complicates matters.
2. As above, but the Factor's Agents have already arrived, and are searching the surface for the actual site when Jamie's scout ship arrives in high orbit.
3. Upon investigation, the player-characters will discover a secret military research facility operating on the surface near the target site. Jamie immediately suspects the base as investigating a Progenitor site. He'll want to search nearby moons and planets for other sites, all while avoiding challenges from military ships launched from the secret base.
4. The Factor's Agents were actually attempting to locate mineral resources needed for her future plans. Although the deposits are of considerable value, Jamie has become obsessed with the belief that there's a Progenitor site somewhere in the system, and will become increasingly difficult to deal with. The Factor's Agents arrive 1d6 days after the team gets there, and further complications arise.
5. As Option 4 above, except that the Factor's Agents arrive with significant military backup. It is their intention that the site of the deposits will be taken by force, if necessary, and aggressively defended against any potential violators or claim-jumpers until the mining ships arrive to begin recovering and processing the raw ore.
6. The team will discover that there is indeed a small Progenitor outpost which has now fallen into ruin, but some portion of it remains intact for exploration. Shortly after the team starts investigating the site, they will activate the outpost's internal defenses. Should the team overcome the internal defenses, the site will set itself to self-destruct with the intention of taking "the Enemy" with it. If the team escapes with anything, it would only consist of what they could carry with them, and would not likely operate once the limited internal power reserves has been consumed. The Factor's Agents arrive 1d6 days later.
Hopefully, this provides an interesting adventure for players to pursue. A third of the options point to natural resources, one to a military site (think Area 51), two to nothing except the right to claim they found a Progenitor site, and one to a small "dungeon crawl" with the classic Collapsing Lair trope, so as to avoid contaminating the campaign with an endless supply of mysterious TL-18 technology that soon won't be so mysterious with that kind of availability. I only put the last one in because I know my players would love the chance to explore such a site. However, for the purposes of setting continuity, the other options are simply better choices.