Telomerase-free cancer cells employ a recombination-based alternative lengthening of telomeres (ALT) pathway that depends on ALT-associated promyelocytic leukemia nuclear bodies (APBs), whose function is unclear. We find that APBs behave as liquid condensates in response to telomere DNA damage, suggesting two potential functions: condensation to enrich DNA repair factors and coalescence to cluster telomeres. To test these models, we developed a chemically induced dimerization approach to induce de novo APB condensation in live cells without DNA damage. We show that telomere-binding protein sumoylation nucleates APB condensation via interactions between small ubiquitin-like modifier (SUMO) and SUMO interaction motif (SIM), and that APB coalescence drives telomere clustering. The induced APBs lack DNA repair factors, indicating that APB functions in promoting telomere clustering can be uncoupled from enriching DNA repair factors. Indeed, telomere clustering relies only on liquid properties of the condensate, as an alternative condensation chemistry also induces clustering independent of sumoylation. Our findings introduce a chemical dimerization approach to manipulate phase separation and demonstrate how the material properties and chemical composition of APBs independently contribute to ALT, suggesting a general framework for how chromatin condensates promote cellular functions.