  Classical conformal blocks naturally appear in the large central charge limit
of 2D Virasoro conformal blocks. In the $AdS_{3}/CFT_{2}$ correspondence, they
are related to classical bulk actions and are used to calculate entanglement
entropy and geodesic lengths. In this work, we discuss the identification of
classical conformal blocks and the Painlev\'e VI action showing how
isomonodromic deformations naturally appear in this context. We recover the
accessory parameter expansion of Heun's equation from the isomonodromic
$\tau$-function. We also discuss how the $c = 1$ expansion of the
$\tau$-function leads to a novel approach to calculate the 4-point classical
conformal block.
