We describe the design and characterization of artificial nucleic acid condensates that are engineered to recruit and locally concentrate proteins of interest in vitro. These condensates emerge from the programmed interactions of nanostructured motifs assembling from three DNA strands and one RNA strand that can include an aptamer domain for the recruitment of a target protein. Because condensates are designed to form regardless of the presence of target protein, they function as "host" compartments. As a model protein, we consider Streptavidin (SA) due to its widespread use in binding assays. In addition to demonstrating protein recruitment, we describe two approaches to control the onset of condensation and protein recruitment. The first approach uses UV irradiation, a physical stimulus that bypasses the need for exchanging molecular inputs and is particularly convenient to control condensation in emulsion droplets. The second approach uses RNA transcription, a ubiquitous biochemical reaction that is central to the development of the next generation of living materials. We then show that the combination of RNA transcription and degradation leads to an autonomous dissipative system in which host condensates and protein recruitment occur transiently and that the host condensate size as well as the time scale of the transition can be controlled by the level of RNA-degrading enzyme. We conclude by demonstrating that biotinylated beads can be recruited to SA-host condensates, which may therefore find immediate use for the physical separation of a variety of biotin-tagged components.