You’re on the right track in terms of setting goals and encouraging staff to work independently, but that’s not enough. Add these activities to help establish yourself as their leader:

• Articulate your vision for the department. Be clear about the goals their work is meant to achieve.
• Be prompt and consistent in making decisions. Then stick to them unless you have good reason to change course. Decisiveness is a good indicator of leadership, and staff will want a degree of predictability.
• Facilitate meetings as an exchange of ideas. Don’t dominate the agenda; solicit input from all present. If you have a lot to say, break it up by inviting questions that lead others to join in. Encourage productive disagreement.
• Set the example with regard to deadlines. Meet yours; respect others’. As soon as you anticipate a delay, tell your staff and adjust the workflow with them.
• Look for everyday opportunities to educate and develop your staff. Always be alert for ways to demonstrate your investment in them.
• Balance the workload so you and your staff are pulling equally toward shared goals. Cross-training will help, but be ready to guide, encourage, pitch in.
• Listen. Keep thinking about what you would need if the roles were reversed.