The integration of terrestrial networks into non-terrestrial networks (NTN) has garnered substantial attention as a transformative approach to extending connectivity to remote and underserved regions. Artificial intelligence (AI) and machine learning (ML) technologies have become crucial enablers of this integration in this environment. They have been specifically integrated into the sixth-generation (6G) architecture to continuously improve coverage effectiveness. With an emphasis on the invaluable contributions of AI/ML to the world of 6G services, this research aims to address the complex issues associated with the integration of terrestrial and non-terrestrial networks. Additionally, it explores different possibilities, with a special emphasis on the practical approaches that AI/ML offer. In order to shed light on the difficulties and problems associated with this integration, the research offers a thorough overview of AI/ML-based solutions that can make it easier for terrestrial networks to be integrated into non-terrestrial networks. The roles of adaptive resource allocation, intelligent routing and handover, autonomous network operation, and effective spectrum management are highlighted in the research. These AI/ML-driven functions act as powerful catalysts, improving non-terrestrial networks performance, maximizing resource use, and improving the seamlessness of connections. Furthermore, they provide networks with the ability to make independent decisions, enhancing overall network efficiency and facilitating optimal spectrum allocation. By providing novel insights and outlining a course for future research projects in this field, this research considerably contributes to the depth of knowledge already known about the use of AI and ML in NTN integration.