Giant stars as known exoplanet hosts are relatively rare due to the potential challenges in acquiring precision radial velocities and the small predicted transit depths. However, these giant host stars are also some of the brightest in the sky and so enable high signal-to-noise ratio follow-up measurements. Here, we report on new observations of the bright (V similar to 3.3) giant star iota Draconis (iota Dra), known to host a planet in a highly eccentric similar to 511 day period orbit. TESS observations of the star over 137 days reveal asteroseismic signatures, allowing us to constrain the stellar radius, mass, and age to similar to 2%, similar to 6%, and similar to 28%, respectively. We present the results of continued radial-velocity monitoring of the star using the Automated Planet Finder over several orbits of the planet. We provide more precise planet parameters of the known planet and, through the combination of our radial-velocity measurements with Hipparcos and Gaia astrometry, we discover an additional long-period companion with an orbital period of similar to 68(-36)(+60) yr. Mass predictions from our analysis place this substellar companion on the border of the planet and brown dwarf regimes. The bright nature of the star combined with the revised orbital architecture of the system provides an opportunity to study planetary orbital dynamics that evolve as the star moves into the giant phase of its evolution.