There were some attempts to come up with some simple ST ship combat systems back in the day.
Rather like the newer Cadet rules, and I think the Commander edition was simplified too.
There was also a version which looked quite good, on one of the Yahoo Groups whose name I forget, which was pretty simple. Sorry, can't recall the name, but perhaps someone here will remember.
It had basic ship templates for the usual TOS ships, as well as the green Klingon Bird of Prey, IIRC.
There were simple rules for quick play engagements.
Alas, with the last computer issue, and the demise of Yahoo Groups, I'm not sure if the rules and ship sheets are still available – they were printed in color, unlike many/most of the older ship sheets I recall, and those looked similar to the Cadet rules system from what little I know of that.
I don't recall an energy allocation system included in that, but there were four quadrants for shield facings – forward, two flanks, and the aft quarter.
I hope someone recalls that and can provide a link to the rules and ship sheets, since I'd like to give them a spin too.