It depends on the author and the agent. I have a lot of clients who will tell me about what they want to write next and might even send me a synopsis or the first pages for my input. But I also have clients who will write something and then send it to me and say “I wrote this, have a look?” and I will have heard nothing about it. Both work fine.
Generally, what's the process after an author comes up with another plot idea and decides to write? After they have an agent, anyways.— Anonymous