  The recent measurements of lepton flavor university (LFU) violating
observables in semileptonic $b \to c \ell \bar{\nu} $ and $b\to s\ell^+ \ell^-$
transitions by various experiments exhibit $(2-3)\sigma$ deviations from their
corresponding Standard Model (SM) predictions. These tantalizing signals hint
towards the possible role of new physics (NP) in $b \to c \tau \bar{\nu}$ and
$b\to s\mu^+\mu^-$ decay channels. This in turn indicates that the same class
of NP as appeared in $b \to c \tau \bar{\nu}$, might also show up in other tree
level processes involving $b \to u \tau \bar{\nu}$ transition. Since these
charged current transitions are doubly Cabibbo suppressed, the NP contributions
could be significant enough leading to sizeable effects in some of the
observables. In this paper, we study the implications of the vector leptoquark
$U_1(3,1,2/3)$, which is one of the few scenarios that can simultaneously
explain the LFU violation signals both in the charged-current as well as
neutral-current sectors, on the semileptonic decays $B \to (\pi, \rho,
\omega)\tau \bar{\nu}$ and $B_s \to (K, K^*) \tau \bar{\nu}$. In particular, we
pay our attention to the branching fraction, lepton flavor non-universality
(LNU) observable, forward-backward asymmetry and the polarization asymmetry
parameters of these modes. We find substantial deviations in the branching
fractions as well as LNU observables of these decay modes due to the $U_1$
contributions, which can be probed by the currently running experiments LHCb
and Belle-II.
