Federated learning (FL) is a collaborative approach where multiple clients, coordinated by a parameter server (PS), train a unified machine-learning model. The approach, however, suffers from two key challenges: data heterogeneity and communication overhead. Data heterogeneity refers to inconsistencies in model training arising from heterogeneous data at different clients. Communication overhead arises from the large volumes of parameter updates exchanged between the PS and clients. Existing solutions typically address these challenges separately. This paper introduces a new communication-efficient algorithm that uses the age of information metric to simultaneously tackle both limitations of FL. We introduce age vectors at the PS, which keep track of how often the different model parameters are updated from the clients. The PS uses this to selectively request updates for specific gradient indices from each client. Further, the PS employs age vectors to identify clients with statistically similar data and group them into clusters. The PS combines the age vectors of the clustered clients to efficiently coordinate gradient index updates among clients within a cluster. We evaluate our approach using the MNIST and CIFAR10 datasets in highly non-i.i.d. settings. The experimental results show that our proposed method can expedite training, surpassing other communication-efficient strategies in efficiency.