  We present a far-ultraviolet (FUV) study of hot stellar populations in the
second parameter pair globular clusters (GCs) M3 and M13, as a part of the
Globular cluster UVIT Legacy Survey program (GlobULeS). We use observations
made with F148W and F169M filters of the Ultraviolet Imaging Telescope (UVIT)
onboard {\em AstroSat} along with ground-based data (UBVRI filters), {\em
Hubble Space Telescope (HST)} GC catalogue, and {\em Gaia} EDR3 catalogue.
Based on the FUV-optical colour-magnitude diagrams, we classify the sources
into the horizontal branch (HB) stars, post-HB stars, and hot white dwarfs
(WDs) in both the GCs. The comparison of synthetic and observed colours of the
observed HB stars suggests that the mass-loss at the red giant branch (RGB) and
He spread in both clusters have a simultaneous effect on the different HB
distributions detected in M3 and M13, such that, HB stars of M13 require a
larger spread in He (${\rm 0.247-0.310}$) than those of M3 (${\rm Y=
0.252-0.266}$). The evolutionary status of HB stars, post-HB stars, and WDs are
studied using SED fit parameters and theoretical evolutionary tracks on the H-R
diagram. We found that the observed post-HB stars have evolved from zero-age HB
(ZAHB) stars of the mass range $0.48-0.55$ \Msun\ in M3 and M13. We detect 24
WD candidates in each cluster having ${\rm \log(L_{bol}/L_\odot)}$ in the range
$-0.8$ to $+0.6$ and ${\rm \log(T_{eff}/K)}$ in the range of 4.2 to 5.0.
Placing the WDs on the H-R diagram and comparing them with models suggest that
M13 has a population of low-mass WDs, probably originating from binary
evolution.
