1. If the issue is affecting only for sending emails,  it simple change the email server IP to a different one so that the websites will be loading  in the old IP and the emails will be routed through the new email server IP.
Before assigning the new email server IP you need to make sure that the whole subnet is not listed.
2. If  the websites may are also affected,  means some ISPs may  label the website as malicious  as if it loading from badly reputed IP/source. 
3. Find the malicious/spam sending account on your  server and resolve it first. Then only spamhause will completely delist your IP.
4. If  you are unable to resolve the issue at expected time,  then as a  last option you can go for a main IP change.
but please  note that there will be down times expected if you change the main IP of the server.
You can change the main IP of the server from WHM/cPanel itself.
- It will affect the DNS resolution for the website and emails, if it affect the name servers too.
-It will affect the cPanel license.
-It will also cause impacts on Seach Engine  ranks of the  websites hosted.
5. Before any  IP changes to  an IP  different subnet, it is better to consult your host to avoid server outages during the process.