An individuals trust levels are enhanced by the behaviors the leaders demonstrate and the processes in place to support individuals do their job better.
Loyalty to you and the organization could be influenced by external factors like team members financial and emotional wellbeing outside of work.
Purpose helps your team to connect at a deeper level with the work they do and the impact it has on the organization and the wider world.
In this sense, Commitment does not mean working long hours for you or your team it means working with integrity and effectiveness.
They are committed to the goals and outcomes their organization values, they are masterful at understanding and working the technical complexities of modern organizations, but they either do not make the time to or do not have the interest in making a commitment to the people.