In this work we present the first implementation of the incremental scheme for coupled cluster linear-response frequency-dependent dipole polarizabilities. The implementation is fully automated and makes use of the domain-specific basis set approach. The accuracy of the approach is determined on the basis of a test suite of 47 molecules and small clusters. The local approximation in the coupled cluster singles and doubles polarizability exhibits a mean error of 0.02% and a standard deviation of 0.32% when using a third-order incremental expansion. With the proposed approach, it is possible to compute polarizabilities with larger basis sets compared to the canonical implementation and thus it is possible to obtain higher total accuracy. The incremental scheme yields the smallest errors for weakly-bound and quasi-linear systems, while two- and three-dimensional (cage-like) structures exhibit somewhat larger errors as compared to the full test set.