New internet connection - email routing

Hi All

We are moving on to a new internet connection, and so are currently planning to move internet, email etc. services across.

We use Office 365 for email (in a hybrid setup), so I am assuming all emails go out through our internet connection using https

I'm wary of being email blacklisted once we move on to the new internet connection, as emails suddenly start appearing from our new public IP address.

Are there any steps I can take to mitigate this, and are there any other changes that need to be accounted for? e.g. MX records, outgoing connectors

Thanks in advance!