So IYTU the IN doesn't send patrols to systems without naval bases? All those gazelles and no training at all in jump drive operation...
IMTU an IN has the duty to send routine patrols to every system in the sub-sector without a base. Usually this is a squadron of gazelles or patrol cruisers, but occasionally it may be a squadron of 1kt-5kt escort class vessels (they need the training too).
I like my games to be tense and unstable, t gives me lots of opportunity to toss my players a cure ball, and gives the more gunfire happy members of the party something to do. It also forces the more thoughtful, and planning sorts problems to work out.
I tend to play my worlds as if it were a very long, very cold war, The Imperium is stretched thin trying to keep control of what it has already, and prevent such groups as the Vargr, Solomani, and Zhodanii from nipping it to death one system at a time.
The fleet has to have a standing force to repel any aggression, but they cant send out a large number of Naval forces without risking an incident.... Think Soviet and US ships nudging and bumping one another during the cold war.
with the situation very tense, and a real possibility of war flaring up over a "Border Dispute" both sides are very nervous when patrols increase, or there are a lot of ships moving about on their frontiers. So there are dead zones, and buffer zones that have little to no official coverage.
while strong Naval Patrols exist, they usually patrol established shipping lanes and conduct random sweeps of systems within one or two jumps of an established trade lane. However they will not go within one or two jumps of a world belonging to another power. so there are pockets where armed ships can refuel, rearm, sell off their loot, and then slip back out to raid sectors that don't have a strong force in the area on a regular basis.
The only Official garrisons in my games are on worlds that have a starport that can support the ships stationed there...repair facilities, fuel refineries, etc... other organisations or local governments fill in where the fleet can't station SDBs or cutters....larger richer sectors can afford to deploy more vessels, while in sectors that aren't as rich or influential patrols are thinner and less organized.
Longer range scout ships, operated by Maritime Assistance ( think an armed version of the coast guard) are employed to check out areas where criminal, or suspect activities have been reported, They look for unusual activity....Such as a larger than average number of armed "merchant" ships congregating in, or loitering in regions with little or no trade.....they also leave behind surveillance devices to track ships moving through an area, and monitor for attacks on merchant shipping when a patrol isn't in the area.
Patrols outside of the normal shipping lanes are usually small, light 'civilian' vessels which have a contract to provide assistance to any ship, in distress or under attack.
Worlds without a full naval presence are allowed to form their own squadrons of fighters and armed small craft as a reserve, or merchant squadron. they usually have a couple of squadrons of thrust 9-12 fighters that can respond to suspicious ships, conduct patrols of the system, etc... They also maintain armed merchant ships..refitted for light combat and customs work. Think a free trader stripped of it's jump drive and fitted with more powerful drives and weapons...or a surplus system boat...
Some worlds will hire Mercenary forces to supplement their own local forces. Worlds without a central government may be protected by local companies, or a corporation/Noble that has interests in the system.
I've ran several games where players were part of a group hired for security, and suppression duties using various types of ships, weapons, and vehicles....Usually they worked for a fairly well off world, or a Noble/corporation who had reasons to want to protect a region of space the Fleet couldn't adequately cover due to location, or political pressures...