High Tc superconducting (HTS) insert in combination with low Tc superconducting (LTS) outsert is the only possibility today to go above 16 T for future high-energy particle accelerator dipoles. These HTS inserts will feature large operating current (≥ 10 kA) and high background fields (≥ 13 T) leading to severe operating conditions. In our 46-turns HTS insert, a 4 × 4 mm twisted stacked cable composed of 20 tapes and carrying 10.4 kA is used. It is simple to manufacture and enables a partial transposition. The designed insert can generate 5 T with good field homogeneity, assuming a homogeneous current density in the cable. However, a half twist per turn applied in the magnet ends of a 15-m-long insert makes it difficult to obtain both low magnetization and uniform current distribution in the cable. Three twisted stacked cables solutions are numerically studied: noninsulated cable, insulated cable, and partially insulated cable. The simulated HTS insert is first submitted to the external field of the outsert then the current is ramped up to nominal value. The partially insulated twisted stacked cable compounds both advantages of noninsulated and insulated cables, and thus appear to be the best solution for the HTS insert.