While this is particularly relevant after the last event (E4 2024, which had… significant PC casualties), I’m hoping it’ll be of use to folks on a more general basis.
And so, one way or another, your character has died. You have processed this in your fashion, and are now moving on, and thinking “what next…?”
(I’m going to assume you still want to play Empire. Other options include different games, or crewing, and those are different topics. 
)
One of the easiest options is to play a very similar character in very similar kit, in your old group. This has the benefit of cost (minimal), required research (minimal) and knowing most of the people (OOC anyway).
As a downside, this does restrict you a little, and can be confusing, both for others (“hey, I’m looking for X who I met before in this group? Isn’t that you?”) and for yourself (“how much of what previous character did can I actually refer to, know, or exploit? Wait, did I tell anyone about that thing?”)
Also, this can be looked at as either a missed opportunity (to explore new concepts and parts of the game) or even a failure of imagination (“can you only think of the one character?”).
Balanced against that, as was recently gently pointed out to me, is that this is not a theatre workshop where you are trying to expand yours skills and repetoire, this is a game that you are paying to play. And if you have fun playing character type A, by all means play another one.
Next on the [moving away from previous character] scale is playing a similar character in a different group, or a different character in the same one. This can have a lot of bonuses, as you still know a good bit about your new skills/setting, but you’ve changed things up a bit so you won’t get recognised, and can explore a bit.
Examples being the Dawnish Knight whose next character is a Highguard Cataphract (seen this done very quickly, they didn’t even get out of the plate armour…), or the Wintermark Thane who returns to their group as a skilled alchemist character (“I’m now going to be supporting you all instead of leading you…”)
And of course, you can throw familiarity to the wind and dive into something completely different! Do you have friends in other nations? See if you can join their group? As whatever you (or indeed they) might like! Empire is a big enough game that switching nations can make it seem very different, open up new parts of the game for you to explore, and start afresh on almost every scale.
Speaking of scales, this is also the time to think about lineage or indeed species 
There are orcs available for play in several nations now…
On a mechanical basis, you can start a new character during the game, courtesy of the computers available at GOD.
(This is, for those unaware, the source of the acronym [Games Operation Desk] and title, as I understand it. “When you die, you report to God, who may send you out with another life.”)
You get a fresh 8 character points for your new character, plus any unspent from your last one (which can be a nice bonus) AND resources as if you’d just started the event as well.
(bear in mind that artisans starting with recipies may have to wait for item ribbons, as GOD needs to print these separately)
On a kit basis, while there are some traders who’ll accept second hand kit, you’re probably better off trying to sell it within your own nation. Some old comrade may like a piece as a keepsake, or some newbie may be overjoyed to get cheap and characterful kit. Weaponry can be trickier (especially if it’s something distinct) but the same applies. This is probably not something that you can do at the event, to be honest…
And finally, you can take a few steps to weave your new character in to the story. Whichever group is your next one, you can make sure they know you’re coming, work out how they might have interacted with your new PC in the past, and perhaps even why their “old friend” hasn’t come to Anvil before. Maybe a personal mission for the new character to draw them in to the ongoing stories, or an interesting piece of group backstory that they can bring to the game? It allows a little smoother introduction all round.
And if you now have a shiny new character coming to the next event, tell us about it! We love to meet new friends, especially if they look similar to our old ones
(Please pipe up with advice, anecdotes, and observations on this!)