Started a webpage that now contains a lot of analytic data. Now that I have the client GA Tracking ID I would like to move the data I already have to that
I think now it's possible to move data from one account to another. Check out this article: https://support.google.com/analytics/answer/6370521?hl=en
If you need to reorganize your properties in Analytics, you can move them (and their views) from one account to another. Moving properties lets you keep your Analytics implementation current with your business. You might be reorganizing after a merger, after an internal restructuring, after hiring a new agency, or you might be developing a new Roll-Up strategy.