We report a new ice phase that forms spontaneously at the interface between ice VII and liquid water in molecular dynamics simulations of TIP4P/2005 water. The new phase is structurally quite similar to an ice phase originally found to be a precursor in the course of the homogeneous nucleation of ice VII in liquid water. A part of the water molecules in these ice phases can rotate easily because the number of hydrogen bonds in them is less than four, and thus they can be regarded as partial plastic phases. A rough estimate suggests that these phases are thermodynamically more stable than either ice VI or ice VII for 3 GPa < P < 18 GPa at T = 300 K. Although the partial plastic phases would be metastable states at any point in the phase diagram of real water, they might be realized experimentally with the aid of dopants and/or solid surfaces.