The non-coding RNA subunit of telomerase provides the template for telomerase activity. In diverse fungi, 3′ end processing of telomerase RNA involves a single cleavage by the spliceosome. Here, we examine how human telomerase RNA (hTR) primary transcripts are processed into the mature form of precisely 451 nt. We find that the splicing inhibitor isoginkgetin mimics the effects of RNA exosome inhibition and causes accumulation of long hTR transcripts. Depletion of exosome components and accessory factors reveals functions for the cap binding complex (CBC) and the nuclear exosome targeting (NEXT) complex in hTR turnover. Whereas longer transcripts are predominantly degraded, shorter precursor RNAs are oligo-adenylated by TRF4-2 and either processed by poly(A)-specific ribonuclease (PARN) or degraded by the exosome. Our results reveal that hTR biogenesis involves a kinetic competition between RNA processing and degradation and suggest treatment options for telomerase insufficiency disorders.