The question in your post is different from the one in the title.

If you want to know if a new therapist will have an access to the old therapist's file, the answer is it depends. If both therapists work at the same agency and you are officially the client of the agency, the therapists can share information without your authorization. If both therapists have private practices, or if one of them is outside of the agency where you were previously receiving the service, nothing about you will be shared without your written permission.

If your question is about whether it'd be necessary for a new therapist to discuss the material from your previous therapy, technically speaking, it's up to you what to work on in therapy, not up to a therapist. Realistically, however, all our issues are essentially the "old issues", or, at least, the new issues are often connected to the old ones. That is to say that with every therapist we still keep working on our "old issues" even though the new ones are often added to that. That's not because we are required to revisit anything, but simply because the old stuff, at least some of it, never goes away..