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The paper aims to construct nonlocal PT-symmetric integrable equations of fourth-order, from nonlocal integrable reductions of a fourth-order integrable system associated with the Lie algebra <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>so</mi><mo stretchy="false">(</mo><mn>3</mn><mo>,</mo><mi mathvariant="double-struck">R</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. The nonlocalities involved are reverse-space, reverse-time, and reverse-spacetime. All of the resulting nonlocal integrable equations possess infinitely many symmetries and conservation laws.