Telomerase is a multi-subunit enzyme that reverse transcribes telomere repeats onto the ends of linear eukaryotic chromosomes and is therefore critical for genome stability. S. cerevisiae telomerase activity is cell-cycle regulated; telomeres are not elongated during G1 phase. Previous work has shown that Est1 protein levels are low during G1 phase, preventing telomerase complex assembly. However, the pathway targeting Est1p for degradation remained uncharacterized. Here, we show that Est1p stability through the cell cycle mirrors that of Clb2p, a known target of the Anaphase Promoting Complex (APC). Indeed, Est1p is stabilized by mutations in both essential and non-essential components of the APC. Mutations of putative Destruction boxes (D-boxes), regions shown to be important for recognition of known APC substrates, stabilize Est1p, suggesting that Est1p is likely to be targeted for degradation directly by the APC. However, we do not detect degradation or ubiquitination of recombinant Est1p by the APC in vitro, suggesting either that the recombinant protein lacks necessary post-translational modification and/or conformation, or that the APC affects Est1p degradation by an indirect mechanism. Together, these studies shed light on the regulation of yeast telomerase assembly and demonstrate a new connection between telomere maintenance and cell cycle regulation pathways.