Non-terrestrial networks (NTN) based on Low Earth Orbit (LEO) satellite constellations are positioned as a foundational component of 6G systems, yet their integration with terrestrial infrastructure presents significant standardization challenges. The 3GPP Network Slice Admission Control Function (NSACF), specified in TS 29.536, currently employs static threshold-based policies that cannot accommodate the dynamic energy constraints inherent to LEO satellite deployments with approximately 90-minute orbital periods and continuous eclipse/sunlight transitions. This paper proposes a QoS-Aware Predictive Admission Control (QAPAC) algorithm that enables AI-native NSACF operation by replacing static threshold-based admission control with predictive admission control using ML-based power consumption forecasting and QoS-driven dynamic threshold adaptation. Experimental evaluation on an emulated 6G NTN testbed demonstrates that QAPAC achieves 100% mission-critical service acceptance compared to 75-76% for baseline methods, with up to 19 percentage point improvement in service availability with high reliability and low latency. These results provide quantitative evidence supporting the evolution of NSACF specifications toward AI-native admission control for 6G systems.