We present the results of 75 As nuclear magnetic resonance (NMR), nuclear quadrupole resonance (NQR), and resistivity measurements in KFe 2 As 2 under pressure ( p ). The temperature dependence of the NMR shift, nuclear spin-lattice relaxation time ( T 1 ), and resistivity show a crossover between a high-temperature incoherent, local-moment behavior and a low-temperature coherent behavior at a crossover temperature ( T ∗ ). T ∗ is found to increase monotonically with pressure, consistent with increasing hybridization between localized 3 d orbital-derived bands with the itinerant electron bands. No anomaly in T ∗ is seen at the critical pressure p c = 1.8 GPa where a change of slope of the superconducting (SC) transition temperature T c ( p ) has been observed. In contrast, T c ( p ) seems to correlate with antiferromagnetic spin fluctuations in the normal state as measured by the NQR 1 / T 1 data, although such a correlation cannot be seen in the replacement effects of A in the A Fe 2 As 2 ( A = K , Rb, Cs) family. In the superconducting state, two T 1 components are observed at low temperatures, suggesting the existence of two distinct local electronic environments. The temperature dependence of the short T 1 s indicates a nearly gapless state below T c . On the other hand, the temperature dependence of the long component 1 / T 1 L implies a large reduction in the density of states at the Fermi level due to the SC gap formation. These results suggest a real-space modulation of the local SC gap structure in KFe 2 As 2 under pressure.