As the stellar core shrinks, it must rotate faster in order to conserve its angular momentum. A rotating object has energy stored in its rotation. The faster the rotation, the more energy. The pulsar is losing energy it radiates energy away that we see in the pulsations. Therefore it should be slowing down.
Careful measurements show that pulsars are very gradually slowing down.
Neutron stars should also have big magnetic fields Recall that electrically conducting fluids tend to trap magnetic field lines. The fluids can move across the field lines only very slowly, and conversely the field lines can move across the fluid only very slowly. The magnetic field lines get concentrated in a smaller surface area, so the magnetic field is stronger. The field rotates with the star. Energetic charged particles can escape along the field lines at the north and south poles.