Anisotropic dark energy model with dynamic pressure anisotropies along different spatial directions is constructed at the backdrop of a spatially homogeneous diagonal Bianchi type V (BV ) space-time in the framework of General Relativity. A time varying deceleration parameter generating a hybrid scale factor is considered to simulate a cosmic transition from early deceleration to late time acceleration. We found that the pressure anisotropies along the y− and z− axes evolve dynamically and continue along with the cosmic expansion without being subsided even at late times. The anisotropic pressure along the x−axis becomes equal to the mean fluid pressure. At a late phase of cosmic evolution, the model enters into a phantom region. From a statefinder diagnosis, it is found that the model overlaps with ΛCDM at late phase of cosmic time.