DNS reverse zone management after ISP change

Hi all,

I tried to google to answer my question, but since I am not sure if my theory is correct, I would appreciate to get a second opinion from the seasoned DNS masters of Reddit.

We are changing our ISP soon and the new ISP is only able to manage the reverse zone. The contract with our current ISP (who also managed our DNS) is valid until September, so our plan is to leave the forward zones with the current ISP until after the major change. We will get new public IPs assigned and the new ISP will take care of the PTR records. We will inform our current ISP of the new IPs so they can update the A records.

Now, I am not sure if I have to inform the current ISP that they have to remove (if that is the correct term) the reverse zones from their management since the new ISP will take this over or if we can just let them know which changes they have to implement for the forward zone and thats it.

I checked our domains in Google dig and couldn't find any PTR records there, so I guess we don't have to specifically tell them to stop managing the reverse zone? I kinda inherited all the infrastructure from a guy who was recently retired and unfortunately neither he nor anyone else could tell me what the current ISP was exactly managing for us in terms of DNS.

What is the best path forward here, so that the change will complete smoothly?

Thanks a lot!