When a player orders a fleet to another planet, the player should be able to give it an additional order to perform when it arrives at the destination (attack planet, invade, transfer all contents down to owned planet, transfer maximum allowable [resource] or [unit] up from owned planet, sell fleet contents to Mesophon, sell fleet to Mesophon, continue on to a different planet).
All fleet orders other than "continue on to a different planet" should be cancelled automatically if the target planet's sovereign changes while the fleet is en route.
It should be possible to change or cancel orders when a fleet is en route and fleets should be dispatched without orders by default. It should also be possible to order fleets to depart at a specific time, rather than immediately. Fleet orders should not be visible to other players, unless they are in a game type with explicit, non-betrayable alliances.
Fleet orders will be especially useful for fleets moving at gunship or capital starship speed. Ship types that take a long time to travel are liable to arrive at their target when the player is AFK and then loiter in orbit, giving an enemy extra time to respond.
In classic Anacreon, starships had initiative while jumpships were exposed for a turn after arrival before they could attack. In the current iteration this dynamic is effectively reversed. Fleet orders would restore some level of balance.
It should not be possible to order fleets to attack a specific other fleet on arrival- I can easily foresee this causing all kinds of bugs. They could maybe be ordered to "attack any hostile fleet" if war/peace conditions were made more explicit.
For extra credit, it could be possible to give fleets a chain of orders to perform in sequence. This could lead to "interesting" or obnoxious outcomes, e.g. a player could build a big, slow attack fleet and order it to gradually conquer and garrison a series of independent or enemy worlds.
It could be possible to set orders to repeat, allowing empires to duplicate R:4021-style trade routes by ordering a transport fleet to repeat moving a bunch of resources to a world that is too distant to be part of the trade network, or to automate repeat sales to Mesophon.
Repeat orders would be a solution to the reinforcement/fleet and infantry consolidation problem.