Cellular senescence is a stable cell cycle arrest that limits the proliferation of pre-cancerous cells. Here we demonstrate that scaffold-attachment-factor A (SAFA) and the long noncoding RNA PANDA differentially interact with polycomb repressive complexes (PRC1 and PRC2) and the transcription factor NF-YA to either promote or suppress senescence. In proliferating cells, SAFA and PANDA recruit PRC complexes to repress the transcription of senescence-promoting genes. Conversely, the loss of SAFA–PANDA–PRC interactions allows expression of the senescence programme. Accordingly, we find that depleting either SAFA or PANDA in proliferating cells induces senescence. However, in senescent cells where PANDA sequesters transcription factor NF-YA and limits the expression of NF-YA-E2F-coregulated proliferation-promoting genes, PANDA depletion leads to an exit from senescence. Together, our results demonstrate that PANDA confines cells to their existing proliferative state and that modulating its level of expression can cause entry or exit from senescence.