Standard sensors make use of radar, normally passive.
All civilian vessels continuously broadcast a transponder signal. It can generally be picked up within 30Mkm with civilian sensors, or 100Mkm with military grade sensors.
Military ships will often switch off their transponders when on a mission, though it is against Imperium law for civilian ships to do so.
The transponder signal carries the ID of the ship, and where it was registered, and has enough information to work out the heading of the vessel.
Starports will generally have high quality sensor arrays that allow them to monitor most of the star system.
They have neutrino sensors which allow them to detect a ship's jump (either out, or in).
The general ranges at which a starport will be aware of what's going on depends on its size. Double these ranges if there is a Naval base present.
Increase by one range band if population is 1 billion+. Increase by 1 range band if TL is 13+. Range bands beyond 30 AU are 60 AU, 100 AU.