  We study the shifted analogue of the "Lie--Poisson" construction for
$L_\infty$ algebroids and we prove that any $L_\infty$ algebroid naturally
gives rise to shifted derived Poisson manifolds. We also investigate derived
Poisson structures from a purely algebraic perspective and, in particular, we
establish a homotopy transfer theorem for derived Poisson algebras. As an
application, we prove that, given a Lie pair $(L,A)$, the space
$\operatorname{tot}\Omega^{\bullet}_A(\Lambda^\bullet(L/A))$ admits a degree
$(+1)$ derived Poisson algebra structure with the wedge product as associative
multiplication and the Chevalley--Eilenberg differential
$d_A^{\operatorname{Bott}}:\Omega^{\bullet}_A(\Lambda^\bullet(L/A))\to
\Omega^{\bullet +1}_A(\Lambda^\bullet(L/A))$ as unary $L_\infty$ bracket. This
degree $(+1)$ derived Poisson algebra structure on
$\operatorname{tot}\Omega^{\bullet}_A(\Lambda^\bullet(L/A))$ is unique up to an
isomorphism having the identity map as first Taylor coefficient. Consequently,
the Chevalley--Eilenberg hypercohomology
$\mathbb{H}(\Omega^{\bullet}_A(\Lambda^\bullet(L/A)),d_A^{\operatorname{Bott}})$
admits a canonical Gerstenhaber algebra structure.
