  In this note, we study a special case of the $4$-pt non-vacuum classical
block associated with the $\mathcal{W}_3$ algebra. We formulate the monodromy
problem for the block and derive monodromy equations within the heavy-light
approximation. Fixing the remaining functional arbitrariness using parameters
of the $4$-pt vacuum $\mathcal{W}_3$ block, we compute the $4$-pt non-vacuum
$\mathcal{W}_3$ block function.
