  Recent pulsar timing observations using MeerKAT of the eccentric binary
millisecond pulsar, PSR J0514$-$4002E, have unveiled a companion with a mass in
the mass gap, ranging from $2.09\, M_\odot$ to $2.71\, M_\odot$. This
challenges conventional astrophysical scenarios for black hole formation. In
this letter, we present an alternative explanation: PSR J0514$-$4002E could be
in a PBH-NS binary, with the companion potentially being a primordial black
hole formed during the early Universe's first-order phase transition. The
associated stochastic gravitational-wave background generated during this phase
transition can account for the observed signal from the pulsar timing array,
and the abundance of primordial black holes is consistent with constraints from
LIGO-Virgo-KAGRA.
