Component of the antigen processing and presentation pathway, which binds to MHC class I coupled with beta2-microglobulin/B2M. Association between TAPBPR and MHC class I occurs in the absence of a functional peptide-loading complex (PLC). {ECO:0000269|PubMed:23401559, ECO:0000269|PubMed:26869717}. This is the function of TAPBPL (TAP binding protein like, ENSG00000139192).