  We construct all possible Weyl invariant actions in $d=4$ for linearized spin
three field in a general gravitational background. The first action is obtained
as the square of the generalized Weyl tensor for a spin three gauge field in
nonlinear gravitational background. It is, however, not invariant under spin
three gauge transformations. We then construct two other nontrivial Weyl but
not gauge invariant actions which are linear in the Weyl tensor of the
background geometry. We then discuss existence and uniqueness of a possible
linear combination of these three actions which is gauge invariant. We do this
at the linear order in the background curvature for Ricci flat backgrounds.
