  Hot Jupiters form an enigmatic class of object with yet unclear formation
pathways. Determination of their occurrence rates as function orbit, planet and
stellar mass, and system age, can be an important ingredient for understanding
how they form. To date, various Hot Jupiters have been discovered orbiting red
giant stars and deriving their incidence would be highly interesting. In this
study we aim to determine the number of Hot Jupiters in a well-defined sample
of red giants, estimate their occurrence rate and compare it with that for A, F
and G-type stars. A sample of 14474 red giant stars, with estimated radii
between 2 and 5 $R_\odot$, was selected using Gaia to coincide with
observations by the NASA TESS mission. Subsequently, the TESS light curves were
searched for transits from Hot Jupiters. The detection efficiency was
determined using injected signals, and the results further corrected for the
geometric transit probability to estimate the occurrence rate. Three previously
confirmed Hot Jupiters were found in the TESS data, in addition to one other
TESS Object of Interest, and two M-dwarf companions. This results in an
occurrence rate of $0.37^{+0.29}_{-0.09}$%. Due to the yet large uncertainties,
this cannot be distinguished from that of A-, F- and G-type stars. We argue
that it is unlikely that planet engulfment in expanding red giants plays yet an
important role in this sample.
