One of the better methods that I've personally found (though it doesn't fit every character concept), is to write the next generation of your character. In this case, after floundering with Triam Akovin towards the end, I eventually decided that her son would succeed her. Now, Cassus has an entirely fresh concept that still respects the continuation of a beloved character, and can take their "twilight years" into unexpected new arcs.
For example, her son's desperation to save his mom from Sickness leads him down some really sketchy paths, and his interaction with Darkwire leads to tragedy for Triam, assumed dead. However, that "death" allowed me to trigger a character concept for her I hadn't had an opportunity for, and now she lives as a resurrected rogue Omni drone currently palling around with Primeval Cults because she doesn't remember who she was (
Koh Su
)
So that leads me to my second method: memory loss. There is a lot of baggage sometimes writing established characters that you have to consider with every post you make. Sometimes the best way to continue on with a beloved character without killing or shelving them is to give them an
entirely new perspective. They don't remember any of that old baggage, all they remember is five minutes before a rancor or whatever is trying to eat them. They don't know about their uber-telekinesis or ultra-lightsaber-rifle. They just know it has teeth, and they want to live. The new relationships will effectively transform your old character into a new one.
Sometimes though, the above concepts just don't work for the type of character you've written that you can't bring yourselves to actually kill off. In that case, just send them Far-Away TM. For my character
Darth Voracitos
, he is the top form of incomprehensible evil and power, so killing him would be a rather big to-do and honestly bothersome. So I "ascend" his interests too far removed places that don't often enough bring him into direct conflict with anything, by giving him a tiny private fiefdom in the Netherworld.
However, if you are
really done with a concept like I was after a year of writing the horrifically disgusting Zambrano the Hutt killing him in an unavoidably permanent way (like obliterating the soul) is The Way. Keep in mind though, even this did not stop me from bringing back the idea of the character. Some years later after his literally permanent unalterable death, I had a Mirror-Dimensional version of Zambrano the Hutt come back as
Zambrano the Starweird
, because Alternate Realities are just as valid as "the main timeline" and have been canonized here on Chaos.
Probably the best way to end a character, IMO, is the simple mundane death. They were doing whatever they were doing, and by circumstances encountered an unavoidably deadly scenario, that reasonably resulted in death, either by someone else's well-coordinated hands or by their own sacrifice. For example, I mentioned Voracitos earlier as this incomprehensible evil and power, but his first death when he was assassinated as the sitting Emperor, his assassin
Caulder Dune
chemically blocked his force connection and caused cardiac arrest, killing him with a heart attack.
So really, ending a character is almost identical to starting one. You have to take the concept in mind, and figure out what the best scenario is to represent that concept effectively.
Have fun!