We report a high-pressure 75 As NMR study on the heavily hole-doped iron pnictide superconductor KFe2As2 (Tc ≈ 3.8 K). The low-energy spin fluctuations are found to decrease with applied pressure up to 2 GPa, but then increase again, changing in lockstep with the pressure-induced evolution of Tc. Their diverging nature suggests close proximity to a magnetic quantum critical point at a negative pressure of P ≃ −0.6 GPa. Above 2.4 GPa, the 75 As satellite spectra split below 40 K, indicating a breaking of As site symmetry and an incipient charge order. These pressure-controlled phenomena demonstrate the presence of nearly-critical fluctuations in both spin and charge, providing essential input for the origin of superconductivity. Heavily doped FeSCs, whose Fermi surfaces are quite different from optimally doped materials, challenge the existing understanding. KFe 2 As 2 has large hole doping (0.5 hole/Fe), but far from being a regular metal it shows heavy-fermion characteristics below a low coherence temperature of order 60 K [8] and superconductivity at a low but finite T c of 3.8 K [9,10]. The absence of electron pockets around (π, π) [11] suggests that spin fluctuations from interband nesting are unlikely, but low-energy electronic correlations are surprisingly strong. Similarly strong low-energy spin fluctuations [12,13] Recent high-pressure studies of KFe 2 As 2 discovered an anomalous reversal of T c , which has a minimum at 1.8 GPa [18]. Scenarios proposed to explain this include a change of pairing symmetry [18,19] and a k z modulation of the superconducting gap [20]. Although spin fluctuations are essential to FeSC superconductivity, no measurements under pressure have yet been reported.In this Letter, we present a high-pressure study of KFe 2 As 2 by nuclear magnetic resonance (NMR). The 75 As spectra and spin-lattice relaxation rate (1/ 75 T 1 T ) are measured under pressures up to 2.42 GPa, revealing three surprising features. First, 1/ 75 T 1 T is dominated by strong low-energy spin fluctuations, suggesting incipient antiferromagnetic order at a quantum critical point near −0.6 GPa. Second, the spin fluctuations show exactly the same reversal behavior as T c , and indeed identical evolution at all pressures. Third, a line splitting of the 75 As satellite spectra below 40 K for pressures above 2.4 GPa indicates a breaking of four-fold symmetry. This effect is caused by charge order, whose fluctuations we propose are strong around the d 5.5 electron filling of KFe 2 As 2 . This emergent charge order is accompanied by the enhancement of spin fluctuations and hence of T c , demonstrating the importance of nearly-critical charge fluctuations in heavily hole-doped FeSCs.Our KFe 2 As 2 single crystals were synthesized by the self-flux method [21]. We measure very large residual resistivity ratios of 1390, indicating extremely high sample quality. We performed high-pressure NMR measurements using a NiCrAl clamp cell, which reaches a maximum pressure of 2.42 GPa at T = 2 K; to obtain a maximally hydrostatic ...