The described technology is generally directed towards network slicing for private cellular networks (PCNs). Network slicing can be leveraged as described herein to meet security requirements and/or other policies applicable to PCNs. Network slices implemented according to this disclosure can comprise a private network slice, a public network slice, and a public safety network slice. User equipment can be provisioned with slice identifiers for the network slices, and applications at the user equipment can specify an appropriate slice identifier for their network communications. Network equipment can be configured to route application traffic to a specified slice and to allocate network resources according to the specified slice, as well as to implement security and other policies according to the specified slice.