We have TFS 2015.
Is there guidance or a mechanism to move Test plans from one Team Project to another Team Project in the same project collection? From poking in MTM, it seems like you can clone a Test Plan, but the dialog does not allow you to specify a different target Team Project for the cloned Test Plan.
Cloning the Test plans with associated Test Suites and Test Cases would also be acceptable if the items cannot physically be moved.
Move a work item to another team project is supported only from Team Services for now. Besides, you can't move work items associated with test management.
There has been a related uservoice for your requirement: Export test plan tree between projects and collections in MTM
We have enabled both Test Plan and Test Suite clone capabilities within the product. See https://msdn.microsoft.com/en-us/library/hh543843.aspx
This allows you to clone test plans/test suites across projects within a collection. For moving artifacts (including test artifacts) across collections, you can use the “TFS Integration Platform toolkit”.
COMPLETED · Visual Studio Team (Product Team, Microsoft Visual Studio)
You could only do this in MTM, could also use Tcm.exe command to copy test suites.