Bringing Clients to a New Agency

I’m looking for advice on how to approach my clients about transitioning to a new agency where I’ll be working. This would involve discussing new terms and potentially higher rates than what they currently have with me.

Once I submit my resignation, I’ll need to hand over the client relationship to someone at my current company. However, I’d prefer to continue working with these clients. Since I haven’t navigated this situation before, I would appreciate any guidance from those with more experience on how to start this conversation and manage the handover process. Thank you!