The right adjoint to the equivariant operadic forgetful functor on incomplete Tambara functors

For $N_{\mathrm{\infty }}$ operads $\mathcal{O}$ and ${\mathcal{O}}^{\mathrm{\prime }}$ such that there is an inclusion of the associated indexing systems, there is a forgetful functor from incomplete Tambara functors over ${\mathcal{O}}^{\mathrm{\prime }}$ to incomplete Tambara functors over $\mathcal{O}$. Roughly speaking, this functor forgets the norms in ${\mathcal{O}}^{\mathrm{\prime }}$ that are not present in $\mathcal{O}$. The forgetful functor has both a left and a right adjoint; the left adjoint is an operadic tensor product, but the right adjoint is more mysterious. We explicitly compute the right adjoint for finite cyclic groups of prime order.