Summary: The concept of extension of a partial isometry, which originally appeared by L. G. Brown and G. K. Pedersen [J. Reine Angew. Math. 469, 113–147 (1995; Zbl 0834.46041)], is discussed more carefully. For \(C^*\)-algebras of real rank zero, an extension property is equivalent to extremal richness or purely infiniteness. We also discuss the relations between extension property and unitary lifting problem.