Helveburg is a nominally neutral world located close to two larger interstellar polities currently in conflict (for convenience, they will be referred to as "the Republic" and "the Federation"). They maintain no interstellar-capable military forces, and planetary defenses are adequate as a symbolic deterrent, but would not be able to stand off a determined attack by either polity. Helveburg's influence on the interstellar scene is mercantile rather than military.
They sit athwart a major trade route to other interstellar states who have no direct contact with either the Federation or the Republic.
The nominal neutrality heavily favors the Republic, to the point where Helveburger mercantile ships will call at Republican ports but not Federation ports. They will routinely allow non-military ships of either polity to dock and be serviced at their facilities; military ships are not permitted to dock except by special prearrangement, if the owning polity does not have a base-facilities agreement with the Helveburg government (the Republic currently does have such an agreement).
The planetary government's unity is only slightly less nominal than their neutrality; every government is a shaky coalition of factions centered on one of the world's many clans. Most governments in recent history have come to power through the realignment of clan alliances, often by violence.
The current government has announced that the base-facilities agreement is open for negotiation. It is expected that the Republic will be able to maintain their base-facilities rights, but the Federation is expected to try to make a case for switching the agreement to them. In any case, negotiations will take months.
The PCs are makeweight extras in the Republic's special mission to renegotiate the base-facilities agreement. They are not part of the crew of the ship that brought them to Helveburg (a Patrol Cruiser or Corsair or equivalent), and most have been added to the mission because of the perceived prestige of their names. Occasionally, they will have to attend formal functions, but most of the time, they will be left to their own devices. All members of the mission are provided housing on the Government Palace grounds at the Helveburg Government's expense, but any mission members wishing to live outside the ground - at their own expense - will readily receive permission. PCs may wish to pursue this option, as it will give them a better feel for the planet, and offer more opportunities for entertainment and enterprise away from the (discreetly) prying eyes of both the Helveburg government and their superiors in the mission. It also offers more opportunity for the PCs to develop contacts who may actually be useful.
At one formal function, a breach in the current coalition, previously well-hidden, becomes open as one of the junior clans in the alliance walks out, taking its collateral clans with it. The function dissolves within minutes, as all high officials present - including the chiefs of the Republic and Federation missions - leave to report the breach to those that need to know.
The following night, the planetary space navy is holding their annual Admiral's Ball, and any PCs of officer rank who have cultivated contacts in that organization will be invited to attend. The Ball is not a government function, but a Navy one, and the Navy has a tradition of holding itself above politics - the breach in the governing coalition has no effect that they will acknowledge.
After the Ball breaks up, at the local social equivalent of about 2AM, any PCs attending will be making their way back to their lodgings. As they pass the port, they will see what looks like smoke come out of all of the open ports of the Republican ship (sleeping gas grenades), and at the same time, armed members of the local militia will start firing at the ship. If the PCs avoid being injured in the initial attack, they will shortly see a grav raft loaded with fully-armored and heavily-armed troops in Federation uniforms exit the hatch of what was ostensibly a Federation freighter. The troops will join the fight on the side of the militia.
At the same time, an attack will be made on the Government Palace by armed militia members, all of whom are from the clans that walked out of the coalition the previous night. The Government is not prepared for this eventuality, and will flee.
The ship will be captured and the crew held in custody in a hastily-converted warehouse on the port grounds. The captain of the Republican ship and all members of the mission whose whereabouts are known will be arrested and interned on the Government Palace grounds; in the confusion, any members not actually on the grounds will be able to avoid capture. If the PCs join the fight at the port, or if they try to prevent the arrest of other members of the mission, they will find themselves arrested and interned as well. The head of the mission and the captain of the Republican ship will be executed as soon as the new government feel that it has solid control of the Palace; further executions will be prevented on Federation orders.
From here, events are up to the PCs and the referee. The planetary government is still in a state of disorganization, so the primary focus of both the new government and the Federation will be to stabilize the situation, possibly with the use of occupation troops. Once stabilization is managed, it is a certainty that the Federation will interrogate the members of the mission, and may well decide to execute them afterward. They will also investigate the Republican ship. No ships have left port since the coup, and none will be permitted to for at least a week.