Coacervates are polymer-rich droplets that form through liquid-liquid phase separation in polymer solutions. Liquid-liquid phase separation and coacervation have recently been shown to play an important role in the organization of biological systems. Such systems are highly dynamic and under continuous influence of enzymatic and chemical processes. However, it is still unclear how enzymatic and chemical reactions affect the coacervation process. Here, we present and characterize a system of enzymatically active coacervates containing spermine, RNA, free nucleotides, and the template independent RNA (de)polymerase PNPase. We find that these RNA coacervates display transient nonspherical shapes, and we systematically study how PNPase concentration, UDP concentration, and temperature affect coacervate morphology. Furthermore, we show that PNPase localizes predominantly into the coacervate phase and that its depolymerization activity in high-phosphate buffer causes coacervate degradation. Our observations of nonspherical coacervate shapes may have broader implications for the relationship between (bio)chemical activity and coacervate biology.