Can you install an EV charger on a shared or private easement driveway?

Not safely, even if the driveway is covered by an easement you hold rights in. An easement's scope is set by the document that created it or the pattern of use by which it was acquired, not by what seems reasonable to you -- and most ingress-and-egress easements don't automatically cover a buried fixed improvement. Get written consent from anyone else with rights in that easement before trenching, separate from whatever the electrical permit requires.

The terms written in the document that created it, or the pattern of use by which it was established -- not a general sense of what seems fair. California's Civil Code states this directly: the extent of a servitude is determined by the terms of the grant or the nature of the enjoyment by which it was acquired. Many states recognize a comparable principle. The recorded easement document for your own driveway, not a general article, is where the real answer is.

No -- they're written for different purposes and typically allow different things. An ingress-and-egress easement grants passage on foot or by vehicle across a described strip of land, and usually says nothing about buried lines. A utility easement is written specifically to allow installing and maintaining lines like conduit, often for a utility company or a shared service. A shared driveway can carry one, both, or neither, depending entirely on what the recorded document actually says -- check the deed records, not the driveway's appearance.

No. A permit confirms the electrical work itself meets code; it says nothing about whether you have the private-law right to install anything on a shared or private easement. Some permit offices ask for proof of legal access before issuing a permit for work on land the applicant doesn't own outright; others don't check at all, which leaves the private-law risk entirely on the homeowner even after a permit is issued and the inspection passes.

Anyone else who holds rights in that same easement, and often the underlying landowner too if the easement crosses land you don't own outright. A shared driveway easement commonly involves at least one neighboring property with rights to use it, and a fixed improvement like buried conduit typically needs that party's written agreement, not just a verbal understanding, because the easement travels with the property through a future sale and an undocumented change can turn into the next owner's dispute.

Three real alternatives, in order of simplicity. Run the circuit entirely within land you own outright, even if that means a longer or more expensive route; negotiate a written easement amendment or license specifically covering the conduit; or check whether an overhead or surface-mounted route avoids the disputed area of the driveway altogether. Price these with an electrician only after the legal question is settled -- routing decisions made before that tend to get redone once consent falls through.