  We report measurements of ac magnetic susceptibility $\chi_{ac}$ and de
Haas-van Alphen (dHvA) oscillations in KFe$_2$As$_2$ under high pressure up to
24.7 kbar. The pressure dependence of the superconducting transition
temperature $T_c$ changes from negative to positive across $P_c \sim 18$ kbar
as previously reported. The ratio of the upper critical field to $T_c$, i.e,
$B_{c2} / T_c$, is enhanced above $P_c$, and the shape of $\chi_{ac}$ vs field
curves qualitatively changes across $P_c$. DHvA oscillations smoothly evolve
across $P_c$ and indicate no drastic change in the Fermi surface up to 24.7
kbar. Three dimensionality increases with pressure, while effective masses show
decreasing trends. We suggest a crossover from a nodal to a full-gap $s$ wave
as a possible explanation.
