Current hyperjump mechanics:
Ship sets course and speed towards destination star. This achieved, and once outside of hyper limit, the ship engages drive, accelerating to at very least 2500 times the speed it had at the moment of activation and departing the physical universe.
When the ship reappears at its destination, it produces a drive flare (detectable by EM sensors), and may suffer brief "sensor blindness", with the worst performing drives causing this effect for 36 hours, although compromising some efficiency for stealth is quite easy- military drives can make much smaller flares and avoid sensor blindness.
What I don't like is sensor blindness. While certainly effective at balancing massive civilian ships with small military ones, it seems a bit off.
While the jump flare makes sense, why not have a much shorter "power drain" state instead of the blindness, where a ship takes somewhere between a few seconds and several minutes (depending on the crew, and the type of engine) to simply get all systems back to full power after the draining conditions of the jump. Additionally, before a jump can occur, the ships must charge the drive, consuming fuel and taking some time before the jump can be made. A civilian ship might take a day or two to fully charge, then take ten minutes to reactivate the maneuvering thrusters, sensors, ect, on the other side. A military drive could ready for a jump in hours or less, and only take a second or two to get the lights on.
The options this would give just for some tactical potentials- ordering your ships to charge jump drives immediately, or have them stay discharged to save fuel, for example. Also, it means that you can't simply fly straight through a series of lined-up systems with nearly no fuel usage- every jump requires some amount of fuel beyond merely correcting the course and maintaining speed.