I am using Visual Studio 2016 with the latest updates. Though I am not the administrator of the project that I am working on, but I have access to creating as many number of Test Plans as required (though i can't delete them once created). I have already created a Master Test Plan, which has like 1000+ test cases, but then we do not need to run all of them everytime. So I was curious if I could create a child test plan under the Master one and include the test cases that are necessary. I only get the green '+'when trying to create a test plan , but nothing to create the child ones.I didn't find any online guide either. Is it actually possible to create one in VSTS?
No, you cannot create the child test plan, it's not supported.
However you can create Test Suites under the test plan, then you can manage the test cases within the specific test suite.
Please see Create a test plan and test suite for detials.
And this article for your reference: Test Planning and Management with Visual Studio Team Services