  We perform a detailed photometric and astrometric analysis of stars in the
Jet stream using data from the first data release of the DECam Local Volume
Exploration Survey (DELVE) DR1 and \emph{Gaia} EDR3. We discover that the
stream extends over $\sim 29 ^{\circ}$ on the sky (increasing the known length
by $18^{\circ}$), which is comparable to the kinematically cold Phoenix, ATLAS,
and GD-1 streams. Using blue horizontal branch stars, we resolve a distance
gradient along the Jet stream of 0.2 kpc/deg, with distances ranging from
$D_\odot \sim 27-34$ kpc. We use natural splines to simultaneously fit the
stream track, width, and intensity to quantitatively characterize density
variations in the Jet stream, including a large gap, and identify substructure
off the main track of the stream. Furthermore, we report the first measurement
of the proper motion of the Jet stream and find that it is well-aligned with
the stream track suggesting the stream has likely not been significantly
perturbed perpendicular to the line of sight. Finally, we fit the stream with a
dynamical model and find that the stream is on a retrograde orbit, and is well
fit by a gravitational potential including the Milky Way and Large Magellanic
Cloud. These results indicate the Jet stream is an excellent candidate for
future studies with deeper photometry, astrometry, and spectroscopy to study
the potential of the Milky Way and probe perturbations from baryonic and dark
matter substructure.
