Demands for greater quality of public services and enhanced efficiency have intensified changes in public organizations. Not surprisingly, these organizations are increasingly searching for new and useful ideas, including disruptive ones, to meet current demands. Whereas previous studies on team radical creativity have focused on the influence that subordinates’ trust in the supervisor has on this type of creativity, this work innovates by testing the leader’s trust in the team as an antecedent. Drawing on Self-Determination Theory, we further add to knowledge by considering the mediating role of team perceived organizational support for creativity and the moderating role of team collaborative climate. The research model was tested with a sample of 228 teams from public organizations with data collected from two sources at three moments in time. We found that the leader’s trust in the team has a direct positive relationship with team radical creativity and an indirect positive relationship with creativity via team perceived organizational support. We also observed that team collaborative climate positively moderates the relationship between the leader’s trust in the team and team radical creativity. These results deliver meaningful theoretical and practical insights into how organizations, especially public ones, can improve team creativity and thus enhance organizational performance.