NA62 has searched for the $K^+ \to \pi^+ \nu \bar{\nu}$ decay using a new kaon decay in-flight technique. One candidate event, compatible with the Standard Model prediction, has been observed from a sample of 1.2 $\times 10^{11}$ decays. Assuming that the event is background, an upper limit of $1.4 \times 10^{-9}$ (95\% CL) has been placed. Prospects for further improvements of the measurement are given.