If you have the original private key on the active certificate, you can install it on the new server or provide it to your new web host. If you do not have the original private key, you will have to reissue your certificate with a new CSR.

Related posts:

I have changed my server, or moved to a different provider; how do I move the certificate? How can I install my SSL certificate on more than one server? What is a private key used for? How do I download my code signing certificate?