What to keep between incarnations
Keeping in mind that the person playing is the same, and we cannot make the real person playing forget how to beat the game... there is little motivation to erase what the character knows.
That is, something you can keep from an incarnation to another is knowledge. For example, learned spells, intrigue, etc. For instance, you may not have the level or energy to cast a spell but you may not have to learn it again, or you could skip the sub plot of figuring out what you need to do and just go do it, and dialog trees that depend on the character having done something already could stay open.
What to lose between incarnations
Evidently, level, iventory, etc... would be lost.
Interestingly, the world is the same. A way to keep stuff could be to have a vault in a bank that is tied to a password, with instructions to give to whoever knows the password, and with some limited space for storage. Using it you could give a few items to your next incarnation.
If the character after reincarnation is different. This means that NPCs does not have to recognize you. If your game have relationships, diplomacy, or similar mechanics, that could be wiped out.
What happens to the character from the old incarnation? You can have a hall of fame in game, a leader board of sorts.
Consider the mechanic of rewinding time in The Legend of Zelda: Majora's Mask.
Aging the characters
You need to be careful about how you affect the character. On one hand you risk it feeling unfair, and on the other some people may like the extra challenge for playing the handicaps of old age.
You see, it is natural that difficulty goes up. You do it too much, and it is unfair, you do it too little and the game is boring. You do it just right and it is engaging. So, do you really want to increase difficulty to motivate people to reincarnate?
If you do, plot wise, characters could have a disease (a curse?), that will give them an unusually short life span. An interesting variant is that this is an unholy dimension that corrupts the characters, or drains their sanity.
I did also consider something else... but it looks more on the engaging side: Going back to the idea of diplomacy and similar systems, you could implement something like the Nemesis System from Middle-earth: Shadow of Mordor. Just like people remember you, enemies might be aware of you and be more aggresive or come better prepared... however that goes away when you reincarnate.
On progression systems
You also have the risk of the playing felling they are being held back in early content. You need to build a healthy progression system, one that does not require the player to waste time learning what they already know, and that does not rely on heavily on grind and random loot.
In fact, does your game need progression? To challenge the assumptions of the question, consider that a game would not suffer from heavy content abandonment if it didn't have a heavy progression system. Getting rid of the progression system would - probably - make people label your game as "casual"... but ther is nothing wrong with that, many "casual" games have high engagement from their players.
So, make the game fun first. If you will have a progression system, make it integral to the game, but not rely on psychological traps... because, the game should be fun first. Done correctly, and players should be able to enjoy staying in the early levels, even if they have already beated the whole game.
Addendum: There is also the issue of balance. If the higher level player leaves nothing to the lower player to do, that is bad. Avoiding the progression system would fix that. Reincarnation - if there is motivation to do it - could fix it too.
See also: My alswer to "Level playing field: Punish the better player or enhance the worse player?".
Motivationt to reincarnate
People can be willing to replay a game on their own, but often they do not what to lose what took them effort to get. Owning a virtual item feels like owning a real item... so, we need a bit of extra encouragement.
Aside from using random generation, and having score and ranking systems...
You could have titles that can only be acquired on the first try, and then use this to tweak the experience. For example NPCs could have different interactions if you have different titles. Futhermore, having some title could prevent you from getting another... now it can interesting to reincarnate to - try to - explore what happens when you get a different set of titles.
- A title for being undefeated.
- A title for finding a pacifist solution to a conflict.
- A title for killing large quantities of enemies.
Alternatively, there could be some meta gaming. Perhaps between reincarnations you go to an afterlife/astral plane where you create your new avatar, and may have the chance to give you special quirks (perhaps some form of blessing or genetic manipulation, perhaps there are secrets/passwords that you can discover in the game and use here). With that, there are thing that you can only get by reincarnation.
It does not have to be an afterlife. Perhaps, it is all in virtual reality, or you are remote controlling avatars, or you could be reliving the memories of an ancestor, or it is time travel... you get the idea.
If anybody can input these secrets/passwords, there would be no motivation to replay. However, I think the game is more interesting if you do not have to get them from the source, but another player can give them to you. One option could be to have a way to share them in game... another would be to have them change them randomly and periodically, so people have to rediscover them.
Consider the reincarnation mechanic of - if you know what it is - Cookie Clicker.
See also: My answer to "Should I worry about Youtube Let's Plays when I'm creating a story-heavy game?", as it has a similar concern: keeping the gameplay interesting even when people already know the plot of the game.
If it applies, I would suggest to ask worldbuilding for implications of people reincarnating. The economy and politic of (your particular brand of) reincarnation could guide your setting. And for your consideration: Is there people in universe that know that reincarnation is a thing?