  We state and prove a simple Theorem that allows one to generate invariant
quantities in Metric-Affine Geometry, under a given transformation of the
affine connection. We start by a general functional of the metric and the
connection and consider transformations of the affine connection possessing a
certain symmetry. We show that the initial functional is invariant under the
aforementioned group of transformations iff its $\Gamma$-variation produces
tensor of a given symmetry. Conversely if the tensor produced by the
$\Gamma$-variation of the functional respects a certain symmetry then the
functional is invariant under the associated transformation of the affine
connection. We then apply our results in Metric-Affine Gravity and produce
invariant actions under certain transformations of the affine connection.
Finally, we derive the constraints put on the hypermomentum for such invariant
Theories.
