Long-period comets are planetesimal remnants constraining the environment and volatiles of the protoplanetary disc. We report the discovery of hyperbolic long-period comet C/2022 E3 (ZTF), which has a perihelion $sim$1.11 au, an eccentricity $gtrsim$1 and an inclination $sim$109$^{circ}$, from images taken with the Palomar 48-inch telescope during morning twilight on 2022 Mar 2. Additionally, we report the characterization of C/2022 E3 (ZTF) from observations taken with the Palomar 200-inch, the Palomar 60-inch, and the NASA Infrared Telescope Facility in early 2023 February to 2023 March when the comet passed within $sim$0.28 au of the Earth and reached a visible magnitude of $sim$5. We measure g-r = 0.70$pm$0.01, r-i = 0.20$pm$0.01, i-z = 0.06$pm$0.01, z-J = 0.90$pm$0.01, J-H = 0.38$pm$0.01 and H-K = 0.15$pm$0.01 colours for the comet from observations. We measure the A(0$^circ$)f$rho$ (0.8~$mu$m) in a 6500~km radius from the nucleus of 1483$pm$40~cm, and CN, C$_3$, and C$_2$ production of 5.43$pm0.11times$10$^{25}$~mol/s, 2.01$pm0.04times$10$^{24}$, and 3.08$pm0.5times$10$^{25}$~mol/s, similar to other long period comets. We additionally observe the appearance of jet-like structures at a scale of $sim$4,000 km in wide-field g-band images, which may be caused by the presence of CN gas in the near-nucleus coma.