  We show that Fronsdal's Lagrangian for a free massless spin-3 gauge field in
Minkowski spacetime is contained in a general Yang--Mills-like Lagrangian of
metric-affine gravity (MAG), the gauge theory of the general affine group in
the presence of a metric. Due to the geometric character of MAG, this can best
be seen by using Vasiliev's frame formalism for higher-spin gauge fields in
which the spin-3 frame is identified with the tracefree nonmetricity one-form
associated with the shear generators of GL(n,R). Furthermore, for specific
gravitational gauge models in the framework of full nonlinear MAG, exact
solutions are constructed, featuring propagating massless and massive spin-3
fields.
