  We report a new hot post-asymptotic giant branch (PAGB) star in the Galactic
globular cluster (GC) E3, which is one of the first of the identified PAGB
stars in a GC to show a binary signature. The star stands out as the brightest
source in E3 in the \mbox{{\em Astrosat}}/UVIT images. We confirmed its
membership with the cluster E3 using Gaia DR3 kinematics and parallax
measurements. We supplemented the photometric observations with radial
velocities (RVs) from high-resolution spectroscopic observations at two epochs
and with ground- and space-based photometric observations from 0.13 $\mu$m to
22 $\mu$m. We find that the RVs vary over $\sim$6 \kms\ between the two epochs.
This is an indication of the star being in a binary orbit. A simulation of
possible binary systems with the observed RVs suggests a binary period of
either 39.12 days or 17.83 days with mass ratio q$\geq$1.0. The [Fe/H] derived
using the high-resolution spectra is $\sim -$0.7 dex, which closely matches the
cluster metallicity. The spectroscopic and photometric measurements suggest
\Teff\ and $\log g$ of the star as 17\,500$\pm$1\,000~K and 2.37$\pm$0.20~dex,
respectively. Various PAGB evolutionary tracks on the Hertzsprung--Russell
(H-R) diagram suggest a current mass of the star in the range 0.51$-$0.55
\Msun. The star is enriched with C and O abundances, showing similar CNO
abundances compared to the other PAGB stars in GCs with the evidence of the
third dredge-up on the AGB phase.
