By the obsolete concept of hybridization, all carbon atoms in graphite are sp2 hybridized. A total of three (1 - 2s and 2 p-orbitals) lead to this hybridization. Due to the formation of sigma bonds with axial overlap of one of these sp2 orbitals with another sp2 orbital of another centre, the atoms exist as a planar array of hexagonal carbon rings. The odd electron resides in the remaining unhybridized p-orbital of sp2 carbon centre, perpendicular to the plane containing the three equivalent sp2 hybrid orbitals. The last odd electron is not localized in the unhybridized p-orbital, but is rather delocalized throughout the layer, due to lateral pπ - pπ, overlap, causing conjugation of odd electron, throughout the plane. It is a bit like an ethylene molecule with H-C bonds replaced by C-C bonds over an enormous plane.
(This is a reason for the high electric conductivity of graphite compared to other carbon allotrophs and other non metals).
Unhybridized p-orbitals (of C atoms in adjacent planes) do not overlap end to end.
In this diagram, the distance between the two adjacent layers of graphite ~0.34 nm (order of 10-9) >>>>>>> greater than the longitudinal length of a lobe of the perpendicular p-orbital projecting from a plane - in the order of picometers (order of 10-12), so clearly they are not large enough to overcome the immense distance of seperation to overlap.
Moreover, the odd electrons in them are already in conjugation, by pπ - pπ lateral overlap. This will further retard any cross-layer bonding interaction.