  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 follow-up measurements. Here we
report on new observations of the bright (V ~ 3.3) giant star $\iota$ Draconis
($\iota$ Dra), known to host a planet in a highly eccentric ~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 ~2%,
~6%, and ~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 ~$68^{+60}_{-36}$ years. Mass predictions from our
analysis place this sub-stellar 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.
