(Review requested)

Thanks for adding this. It might be better to use access=private rather than access=no here - see https://wiki.openstreetmap.org/wiki/Key:access#List_of_possible_values

If you wanted, you could also split the road at the gate and add access=private to the section behind it.

The military area itself might benefit from a hazard=unexploded_ordnance or hazard=shooting_range tag (see https://wiki.openstreetmap.org/wiki/Key:hazard ) if you're confident that the warning on the gate applies to the whole area.