With the advent of large-scale models and their success in diverse fields, Knowledge Distillation (KD) techniques are increasingly used to deploy them to edge devices with limited memory and computation constraints. However, most distillation works focus on improving the prediction performance of the student model with little to no work in studying the effect of distillation on key fairness properties, ensuring trustworthy distillation. In this work, we propose a fairness-driven distillation framework, BIRD (BIas-awaRe Distillation), which introduces a FAIRDISTILL operator to collect feedback from the student through a meta-learning-based approach and selectively distill teacher knowledge. We demonstrate that BIRD can be augmented with different KD methods to increase the performance of foundation models and convolutional neural networks. Extensive experiments across three fairness datasets show the efficacy of our framework over existing state-of-the-art KD methods, opening up new directions to develop trustworthy distillation techniques.