Binds directly to 5'-TTAGGG-3' repeats in telomeric DNA (PubMed:23685356, PubMed:23813958). Associates with the telomerase complex at sites of active telomere processing and positively regulates telomere elongation (PubMed:23685356). Important for TERT binding to chromatin, indicating a role in recruitment of the telomerase complex to telomeres (By similarity). Also plays a role in the alternative lengthening of telomeres (ALT) pathway in telomerase-negative cells where it promotes formation and/or maintenance of ALT-associated promyelocytic leukemia bodies (APBs) (PubMed:23813958). Enhances formation of telomere C-circles in ALT cells, suggesting a possible role in telomere recombination (PubMed:23813958). Might also be involved in the DNA damage response at telomeres (PubMed:23813958). {ECO:0000250|UniProtKB:Q8BJA3, ECO:0000269|PubMed:23685356, ECO:0000269|PubMed:23813958}. This is the function of HMBOX1 (homeobox containing 1, Ensembl gene identifier ENSG00000147421).