Opportunities for the Nation and States to Harness Onshore Resources for Energy Act or the ONSHORE Act This bill makes various changes to expand and otherwise addresses onshore oil and gas resources on federal land and non-federal surface estates. Specifically, the bill requires, subject to some limits, the Department of the Interior and the Forest Service to lease certain public lands and Forest System land with known or potential oil or gas deposits. (Current law authorizes but does not require leasing.) Other changes in the bill include (1) allowing Interior to delegate authority over certain federal permitting and other regulatory responsibilities for oil and gas leases to states; (2) exempting some oil and gas activities conducted on non-federal surface estates from certain permitting and environmental review requirements; and (3) requiring deference to state regulations, guidance, and permit requirements for all activities regarding hydraulic fracturing (a type of process used to extract underground energy resources) on federal land.