  The incompatibility of the measurements constraints the achievable precisions
in multi-parameter quantum estimation. Understanding the tradeoff induced by
such incompatibility is a central topic in quantum metrology. Here we provide
an approach to study the incompatibility under general $p$-local measurements,
which are the measurements that can be performed collectively on at most $p$
copies of quantum states. We demonstrate the power of the approach by
presenting a hierarchy of analytical bounds on the tradeoff among the precision
limits of different parameters. These bounds lead to a necessary condition for
the saturation of the quantum Cram\'er-Rao bound under $p$-local measurements,
which recovers the partial commutative condition at p=1 and the weak
commutative condition at $p=\infty$. As a further demonstration of the power of
the framework, we present another set of tradeoff relations with the right
logarithmic operators(RLD).
