We study linear regression models with clustered data, high-dimensional controls, and a complicated structure of exclusion restrictions. We propose a correctly centered internal IV estimator that accommodates a variety of exclusion restrictions and permits within-cluster dependence. The estimator has a simple leave-out interpretation and remains computationally tractable. We derive a central limit theorem for its quadratic form and propose a robust variance estimator. We also develop inference methods that remain valid under weak identification. Our framework extends classical dynamic panel methods to more general clustered settings. An empirical application of a large-scale fiscal intervention in rural Kenya with spatial interference illustrates the approach.