With eukaryotic genome replication, incomplete telomere synthesis results in chromosome shortening and eventual compromise of genome stability. Telomerase counteracts this terminal sequence loss by synthesizing telomeric repeats through repeated cycles of reverse transcription of its internal RNA template. Using human telomerase domain-complementation assays for telomerase reverse transcriptase protein (TERT) and RNA in combination with the first direct footprinting assay for telomerase association with bound DNA, we resolve mechanisms by which TERT domains and RNA motifs direct repeat synthesis. Surprisingly, we find that product-template hybrid is sensed in a length- and sequence-dependent manner to set the template 5' boundary. We demonstrate that the TERT N-terminal (TEN) domain determines active-site use of the atypically short primer-template hybrid necessary for telomeric-repeat synthesis. Also against expectation, we show that the remainder of TERT (the TERT ring) supports functional recognition and physical protection of single-stranded DNA adjacent to the template hybrid. These findings establish unprecedented polymerase recognition specificities for DNA-RNA hybrid and single-stranded DNA and suggest a new perspective on the mechanisms of telomerase specialization for telomeric-repeat synthesis.