  We formulate Nazarov-Wenzl type algebras ${\widehat{P}_d^-}$ for the
representation theory of the Periplectic Lie superalgebras $\mathfrak{p}(n)$.
We establish a Arakawa-Suzuki type theorem to provide a connection between
$\mathfrak{p}(n)$-representations and $\widehat{P}_d^-$-representations. We
also consider various tensor product representations for $\widehat{P}_d^-$. The
periplectic Brauer algebra $A_d$ defined by Moon is an quotient of
$\widehat{P}_d^-$. In particular, actions induced by Jucys-Murphy elements can
be obtained under the tensor product representation of $\widehat{P}_d^-$. Also,
a Poincare-Birkhoff-Witt type basis for $\widehat{P}_d^-$ is obtained.
