Trust means follow through. It is a combination of a perception of character and a reflection of character itself. It is also an instinctual feeling; that a leader can be relied on regardless of circumstances. The core of trust is predictability on the part of the leaders .
Different levels of trust exist, however, according to a Harvard Business Review article by Robert Galford and Anne Seibold Drapeau. Strategic trust is the type people have in their senior leadership to make the right decisions. Personal trust is the type people have in their immediate managers. Organizational trust is the type that people have in their institution.  Project managers, of course, should concern themselves with developing and maintaining personal trust. However, the quality of strategic and organizational trust can also impact how well people trust their project managers.
Generating trust, of course, does not often arise spontaneously. It is earned by the leader and can be accumulated as it is earned.  Trust is also earned through personal interactions. 
Leaders must not only earn the trust of subordinates , but they must also demonstrate their trust in others. They will gain an important benefit by their willingness to trust others. They will become more tolerant of different ideas and actions. Leaders who demonstrate trust will consider many perspectives and will be willing to allow others to influence their decisions.
Trust is the third cornerstone of credibility and, in the end, the most important of them. If project managers violate trust bestowed by stakeholders, their credibility can decline quite rapidly . Fortunately, project managers can earn and sustain trust in many ways.
They must be straightforward with all stakeholders in all dealings, that is, "tell it like it is." People trust others, especially leaders, who reveal their positions and act with thorough-through, thereby building trust.
If a project cannot meet all its goals and objectives, for example, project managers should be honest about the circumstances. Unfortunately, for reasons of pride or to avoid complicating relationships, many project managers will not admit a problem exists. Instead, they may present explanations that create a facade that everything is fine when, in reality, nothing is going well. Often, they rationalize to themselves that "things will improve with time." The danger is that improvements in performance may not occur, surprising stakeholders at the last minute. Once that happens, project managers lose the trust granted to them.
Project managers must empower and delegate. To gain and maintain trust, project managers must also exhibit trust in others. They must avoid controlling too closely, or micromanaging, others, e.g., "looking over their shoulders." That means leaders must create an environment that augments people's confidence that, in turn , encourages risk taking. The emphasis can then shift from blaming to learning. 
Project managers, instead, must empower team members and delegate tasks to them. Failure to do so only exhibits their distrust in others that, in turn, generates distrust . Effective project managers must demonstrate trust in others if they want to be trusted.
They must be fair in all dealings. They must avoid even the appearance of taking sides. Otherwise , they will reduce their opportunities to strive for objectivity and receive the active contributions from team members. Unseasoned project managers often find themselves viewing stakeholders as "good vs. bad guys." When that happens, cooperation breaks down and marginal contributions of team members follow. Even more importantly, they and everyone else lose trust.
Two of the best ways to maintain fairness in dealings with stakeholders:
Focus on the goals and objectives of their projects. When a contentious issue arises, project managers should frame it from the context of the goals and objectives.
Concentrate on facts and data that relate to an issue. Project managers must avoid treating assumptions and values as facts and data; otherwise, some stakeholders will view projects managers as taking sides.
Project managers should respect all stakeholders in dealings. Project managers should recognize that everyone has an important role, albeit small, on a project. While some stakeholders contribute more than others, project managers should avoid ignoring and even disregarding the work of others who may not be major contributors. Making people feel that they are unimportant or insignificant often generates negative consequences, e.g., treating performance or deliverables in kind. If project managers have respect for others and their work, stakeholders will exhibit more trust because they will feel more comfortable in trusting them with their insights and comments.
They must manage themselves as well as others. Project managers must "walk the talk." They must exhibit what they say if they hope to earn trust. There is wide agreement among leadership experts in this regard. In Leaders , Bennis and Nanus note that not managing oneself can harm a leader's effectiveness and that of others.  Michael Abrashoff agrees and further observes that people look on leaders as role models. As such, a leader must exhibit strengths reflective of courage, integrity, accountability, authenticity, and good judgment. 
If project managers do not "practice what they preach" they will be seen as people who heed their own words because it raises the simple question ” if project managers are not consistent in action, then how can they be trusted in other matters, e.g., being truthful with oneself. Project managers must live by the very beliefs and values that they expect others to hold if they expect people to trust them.
Project managers must maintain confidentiality. Nothing is worse than telling someone something in confidence only to find that it has been leaked to other people. If people are to disclose needs and feelings, leaders must create a "climate of trust" through caring. 
For example, a team member talks to a project manager about the performance of a colleague. The project manager then talks to someone else about the discussion in such a way that reveals the identity of the person who raised the issue. When that happens and becomes known, people will reluctantly share any other thoughts or information with the project manager. Trust collapses over this incident and likely for the remainder of the project.
They must respect people's needs and wants via personal understanding. Covey says that helps to overcome barriers to performance on individual and group levels. The reason is because it encourages openness. 
Project managers who understand the importance of this facet of respect will see people placing their faith and trust in them. They will likely share information and go to them on other issues; they see the project manager as someone to approach rather than to avoid. In other words, to use a phrase popularized by the psychologist Carl Rogers, project managers are seen as builders of bridges, not walls.
 Robert Galford and Anne S. Drapeau, The enemies of trust, Harvard Business Review , pp. 89 “95, February 2003.
 Warren Bennis and Burt Nanus, Leaders , Perennial Library, New York, 1985, p. 153.
 James M. Kouzes and Barry Z. Posner, The Leadership Challenge , Jossey-Bass, San Francisco, 1987, p. 151.
 James M. Kouzes and Barry Z. Posner, Ten lessons of leadership, in A Systems Approach to Small Group Interaction , 6th ed., Stewart L. Tubbs, Ed., McGraw-Hill, Boston, 1997, pp. 197 “198.
 Warren Bennis and Burt Nanus, Leaders , Perennial Library, New York, 1985, p. 56.
 Abrashoff, Michael D., Playing to win: ten principles of grassroots leadership, Seminar for Living Leadership , 2003, p. 63.
 James M. Kouzes and Barry Z. Posner, Ten lessons of leadership, in A Systems Approach to Small Group Interaction , 6th ed., Stewart L. Tubbs, Ed., McGraw-Hill, Boston, 1997, p. 197.
 Stephen R. Covey, The Seven Habits of Highly Effective People , Simon & Schuster, New York, 1990, p. 151.