We explore the response of Ir
5
d
orbitals to pressure in
β
−
Li
2
IrO
3
, a hyperhoneycomb iridate in proximity to a Kitaev quantum spin-liquid (QSL) ground state. X-ray absorption spectroscopy reveals a reconstruction of the electronic ground state below 2 GPa, the same pressure range where x-ray magnetic circular dichroism shows an apparent collapse of magnetic order. The electronic reconstruction, which manifests a reduction in the effective spin-orbit interaction in
5
d
orbitals, pushes
β
−
Li
2
IrO
3
further away from the pure
J
eff
=
1
/
2
limit. Although lattice symmetry is preserved across the electronic transition, x-ray diffraction shows a highly anisotropic compression of the hyperhoneycomb lattice which affects the balance of bond-directional Ir-Ir exchange interactions driven by spin-orbit coupling at Ir sites. An enhancement of symmetric anisotropic exchange over Kitaev and Heisenberg exchange interactions seen in theoretical calculations that use precisely this anisotropic Ir-Ir bond compression provides one possible route to the realization of a QSL state in this hyperhoneycomb iridate at high pressures