Tight integration between classical and quantum networking requires strict synchronization of events between the classical and quantum portions of the network. Time-Sensitive Networking (TSN) as defined by IEEE 802.1Q is limited to accuracy on the order of microseconds due to limitations in time synchronization performance; TSN gate control is thus similarly limited. This work presents a new High-Precision TSN that enables greater accuracy and resolution toward sub-nanosecond TSN gate control and can directly support entanglement distribution, a key component in a software-designed quantum network architecture where classical control can reach deep into the quantum network and directly control time critical operations.