Leadership has been extensively discussed for a long time in the literature by describing the ideal traits of a leader, emphasizing the positive influence of the good leader on group, team, and organization performance. Although many different types and traits of leadership have been proposed, little work has considered the pivotal fact that the leader has limited capacity and resources (e.g., cognition, time, energy) when dealing with numerous time sensitive tasks in real, dynamic settings. This work is interested in how the leader can provide effective feedback to improve a follower's team performance for establishing long-term assets in the team, while maximizing the utilization of limited resources. To this end, we adopt the Instance-Based Learning (IBL) cognitive architecture to develop a leadership framework that determines whether to provide feedback to a follower, and if so, how much feedback should be provided depending on the follower's level of performance readiness. This proposed framework aims to maximize the trust improvement of followers, while minimizing the cost spent in providing feedback to achieve cost-effective decision making. By reflecting the concept of situational leadership, our proposed framework allows the leader to respond adaptively to followers based on their readiness. Our simulation results show that the proposed IBL-based framework provides an appropriate level of adaptive feedback depending on the readiness of a follower given no prior knowledge about the followers, while the leader can make cost-effective decision in feedback provision. Such cognitive leadership framework can be useful as a cognitive inspired decision aid tool for a human leader, or part of an autonomous and adaptive feedback system.