A project team has the right to expect the Project Manager to lead them. Leadership does not always mean hand holding, and it does not always mean full delegating. It means that you care about what is happening, you provide guidance and vision, you support, coach, train your team.
You look for opportunities to advance your team members, or your project, or your customer toward what they value. You freely share your knowledge, wisdom and skills in pursuit of the objective. You inspire others to do the same.
Your loyalty should be with your Charter; this is your objective. Your strategy is to deliver your project outputs on time and on budget. Your greatest tactic to do this is to lead, inspire, engage and guide.
Leadership should (IMHO) be biased toward recognition and reward, and away from punishment. We can punish people into obedience, threaten them into compliance – but we must lead them into true performance. Since this is best for your project – it should be your “go to” position.
Not sure what leadership is? There are hundreds, thousands of resources on how to be a leader. Go find them, read them, apply them. Be sincere and honest. The rewards are fantastically greater then the effort you will put in.