A lot depends on how you are moving CRM:
Scenario 1:
If you are making a copy of the organization database and importing the organization into the CRM Deployment Manager in the new environment, then the database will contain the ClickDimensions solution. We would just have to update your account so it connects to the new CRM environment. Our support team can do that for you in a support ticket.
In this scenario, you cannot have two concurrently functioning solutions because our solution includes an embedded AccountKey, and that AccountKey determines which CRM our cloud application will connect to. So if you move the organization database to a new environment, and we update the account to connect to the new environment, the old one would no longer work.
Scenario 2:
If you are migrating data from the old CRM to the new one using a tool like Scribe, then you will need to register the new CRM environment and receive a new solution file. Contact your account manager for the link to register. Keep in mind that not all ClickDimensions items may be able to be migrated since there are items that depend on integration with the correct Account Key. Some things can be migrated with our Export/Import tool. See here: http://blog.clickdimensions.com/2012/01/migrating-clickdimensions-settings-across-different-crm-deployments.html
Other Scenarios:
If you are using some other scenario to move to the new environment (such as making a copy of a virtual machine), let us know and we'll do our best to help!