Integration with Campaign Monitor?
it is certainly possible to export and import from another system, as long as campaign monitor has some kind of rest api, it should be fairly easy to develop.

however, and no matter the external service you want to integrate to, you would need to clarify better what needs to be pushed and pulled. what constituent details? only the email, the full name...

and then you have the problem of when to synchronise and who has the master data. eg. what happens if the first name changes in civi, what happen if the email changes in campaign monitor? what happen if the email changes in both...

lots of questions and potential conflicts you need to resolve to be able to clarify the behaviour of your system. these are hard problems, and bidirectional sync is potentially really complex. try to simplify as much as you can, eg all data in civi is the master one and considered the most up to date.

please clarify what you want to synchronise and how often, it will help giving a less generic answer