Nikon published firmware updates for older DSLRs on 27th of February. Those updates for D4, D4s, Df, D800, D800E, D810, D810A, D7100 and D7200 should provide compatibility for AF-P lenses. Without firmware update, the stepping motor returns to its default position once the light meter turns off.
Shortly after some people updated, complaints about the autofocus on older Sigma lenses popped up. The AF function simply stopped to work. I was able to confirm this on D4 and D800 with a Sigma 150mm 2,8 macro lens (non-OS), which was simply dead after the update.
Fortunately Nikon still provides the older firmware versions for download and a downgrade is possible without any problem. For people not using AF-P lenses an update is therefore not recommended.