To start a new conversation, tap the compose icon in the top right of the conversations drawer, or tap the chat icon in the navigation bar.
Each conversation is a fresh start
New conversations begin fresh - Sol won't carry the thread of your previous conversation into a new one. But if you have an account with memory enabled, he carries his broader knowledge of you. The new conversation starts without the old thread, but not without context.
Your previous conversations are saved
Starting a new conversation doesn't remove previous ones. All your conversations are stored in the conversations drawer and can be returned to at any time.