Transports dicarboxylates across the inner membranes of mitochondria by a counter-exchange mechanism (PubMed:11083877). Can transport 2-oxoadipate (2-oxohexanedioate), 2-oxoglutarate, adipate (hexanedioate), glutarate, and to a lesser extent, pimelate (heptanedioate), 2-oxopimelate (2-oxoheptanedioate), 2-aminoadipate (2- aminohexanedioate), oxaloacetate, and citrate (PubMed:11083877). Plays a central role in catabolism of lysine, hydroxylysine, and tryptophan, by transporting common metabolite intermediates (such as 2-oxoadipate) into the mitochondria, where it is converted into acetyl-CoA and can enter the citric acid (TCA) cycle (Probable). {ECO:0000269|PubMed:11083877, ECO:0000305|PubMed:11083877, ECO:0000305|PubMed:29517768}. This is the function of SLC25A21 (solute carrier family 25 member 21, Ensembl gene identifier ENSG00000183032).