Telomerase maintains ends of eukaryotic chromosomes, telomeres. Telomerase loss results in replicative senescence and a switch to recombination-dependent telomere maintenance. Telomerase insufficiency in humans leads to telomere syndromes associated with premature ageing and cancer predisposition. Here we use yeast to show that the survival of telomerase insufficiency differs from the survival of telomerase loss and occurs through aneuploidy. In yeast grown at elevated temperatures, telomerase activity becomes limiting: haploid cell populations senesce and generate aneuploid survivors--near diploids monosomic for chromosome VIII. This aneuploidy results in increased levels of the telomerase components TLC1, Est1 and Est3, and is accompanied by decreased abundance of ribosomal proteins. We propose that aneuploidy suppresses telomerase insufficiency through redistribution of cellular resources away from ribosome synthesis towards production of telomerase components and other non-ribosomal proteins. The aneuploidy-induced re-balance of the proteome via modulation of ribosome biogenesis may be a general adaptive response to overcome functional insufficiencies.