action, we now apply the method of [@Concha:2016zdb], which consists in rescaling not only the generators but also the coefficients appearing in the invariant tensor before applying a contraction, in order to end up with a non-trivial invariant tensor for the contracted (super)algebra on which the desired CS theory will be based. Precisely, we consider the non-vanishing components of the invariant tensor for $\mathfrak{osp}(2|1)\otimes \mathfrak{sp}(2)$ given in and rescale not only the generators in compliance with but also the coefficients appearing in as follows: $$\alpha_0 \rightarrow \alpha_0 \,  , \quad \alpha_1 \rightarrow \sigma \alpha_1 \, .$$ In this way, taking the limit $\sigma \rightarrow \infty$, we end up with the following non-vanishing components of the invariant tensor for the AdS Carroll superalgebra: $$\label{invadscarrollsuper}
\begin{split}
& \langle J_{ab} J_{cd} \rangle = \alpha_0 \left( \delta_{ad} \delta_{bc} - \delta_{ac} \delta_{bd} \right) \, , \quad 
\langle J_{ab} H \rangle = \alpha_1 \epsilon_{ab} \, , \quad 
\langle K_a P_b \rangle = - \alpha_1 \epsilon_{ab} \, , \quad
\langle P_{a} P_{b} \rangle = \frac{\alpha_0}{\ell^2} \delta_{ab} \, , \\
& \langle Q_\alpha Q_\beta \rangle = 2 \alpha_1  C_{\alpha \beta} \,  .
\end{split}$$

Thus, using the connection $1$-form in and the non-vanishing components of the invariant tensor given 