The phylum Actinomycetota and genus Streptomyces in particular are the major source for discovery of natural products with diverse chemical structures and a variety of biological activities. Genes encoding biosynthetic pathways for bacterial natural products are grouped together into biosynthetic gene clusters (BGCs). The size of a typical actinobacterial BGC may range from 10 kb to 200 kb, which makes their cloning for heterologous expression a challenging task. Various DNA cloning and assembly methods have been established for capturing BGCs. Among them, the transformation‐associated recombination (TAR) in Saccharomyces cerevisiae remains one of the most cost‐effective, accessible, customisable and precise approaches. However, the drawback of TAR cloning is a need for intensive screening of clones in order to identify one carrying the BGC. In this study, we report a further development of the TAR cloning approach by introducing the direct selection of colonies with BGC of interest based on the yeast killer phenomenon. For this, a new TAR cloning vector system was constructed and the strategy was validated by successful cloning of chelocardin (35 kb) BGC from Amycolatopsis sulphurea and daptomycin BGC (67 kb) from Streptomyces filamentosus. Both BGCs were functionally expressed in a heterologous host, resulting in the production of the corresponding antibiotics. The proposed approach could be widely applied for precise direct cloning of BGCs from the representatives of phylum Actinomycetota and easily adopted for other bacteria.