There is, but your wish of "clean" is ambiguous.

With clean I mean the opposite of how I currently do it, which is by asking the model to compact the whole thread into a prompt which will act as context for next model.

My way of prompting this varies and every time I receive the blob of output, I can’t fell how well it managed to capture the necessary details. This way feels lika a dirty way to transfer knowledge from one conversation to another.

You said there is? What’s the options?

Here's a view for "clean:"

1. Every chat should have a context used/remaining measurement so you know when you have to ditch the current chat for a fresh one.

2. Every chat should analyze and categorizes each element of context by how useful it is towards the overarching goal of the chat.

3. Every chat has a handoff button with a "usefulness" slider (say 1-5) that shows the total size of the context based on its setting.

4. The handoff automatically creates a new chat with the desired amount of context and a prompt to get it back to where you were.

That said, I am newb and so there is some reason why these non-deterministic LLMs can't do this :-/