In speaker verification, contrastive learning is gaining popularity as an alternative to the traditionally used classification-based approaches. Contrastive methods can benefit from an effective use of hard negative pairs, which are different-class samples particularly challenging for a verification model due to their similarity. In this paper, we propose CHNS - a clustering-based hard negative sampling method, dedicated for supervised contrastive speaker representation learning. Our approach clusters embeddings of similar speakers, and adjusts batch composition to obtain an optimal ratio of hard and easy negatives during contrastive loss calculation. Experimental evaluation shows that CHNS outperforms a baseline supervised contrastive approach with and without loss-based hard negative sampling, as well as a state-of-the-art classification-based approach to speaker verification by as much as 18 % relative EER and minDCF on the VoxCeleb dataset using two lightweight model architectures.