The transit method of exoplanet discovery and characterization has enabled numerous breakthroughs in exoplanetary science. These include measurements of planetary radii, mass-radius relationships, stellar obliquities, bulk density constraints on interior models, and transmission spectroscopy as a means to study planetary atmospheres. The Transiting Exoplanet Survey Satellite (TESS) has added to the exoplanet inventory by observing a significant fraction of the celestial sphere, including many stars already known to host exoplanets. Here we describe the science extraction from TESS observations of known exoplanet hosts during the primary mission. These include transit detection of known exoplanets, discovery of additional exoplanets, detection of phase signatures and secondary eclipses, transit ephemeris refinement, and asteroseismology as a means to improve stellar and planetary parameters. We provide the statistics of TESS known host observations during Cycle 1 & 2, and present several examples of TESS photometry for known host stars observed with a long baseline. We outline the major discoveries from observations of known hosts during the primary mission. Finally, we describe the case for further observations of known exoplanet hosts during the TESS extended mission and the expected science yield.
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