T-cell receptors (TCRs) encode clinically valuable information that reflects prior antigen exposure and potential future response. However, despite advances in deep repertoire sequencing, enormous TCR diversity complicates the use of TCR clonotypes as clinical biomarkers. We propose a new framework that leverages experimentally inferred antigen-associated TCRs to form meta-clonotypes – groups of biochemically similar TCRs – that can be used to robustly quantify functionally similar TCRs in bulk repertoires across individuals. We apply the framework to TCR data from COVID-19 patients, generating 1831 public TCR meta-clonotypes from the SARS-CoV-2 antigen-associated TCRs that have strong evidence of restriction to patients with a specific human leukocyte antigen (HLA) genotype. Applied to independent cohorts, meta-clonotypes targeting these specific epitopes were more frequently detected in bulk repertoires compared to exact amino acid matches, and 59.7% (1093/1831) were more abundant among COVID-19 patients that expressed the putative restricting HLA allele (false discovery rate [FDR]<0.01), demonstrating the potential utility of meta-clonotypes as antigen-specific features for biomarker development. To enable further applications, we developed an open-source software package, tcrdist3, that implements this framework and facilitates flexible workflows for distance-based TCR repertoire analysis.