In this study, the fundamental problem of the ignition of a kerosene single droplet in a quiescent medium at engine high-altitude relight conditions is investigated using numerical simulations. The main objective is to improve the understanding of ignition phenomena with a focus on the effect of droplet evaporation in determining the growth of the ignition kernel and flame establishment. Results show that when the droplet is fully immersed in a high temperature region, ignition occurs when the scalar dissipation rate associated with evaporation decreases enough to allow the initiation of a flame. The ignition time depends on the droplet diameter and the far field temperature, i.e. the position of the droplet with respect to the spark location. As the fuel is consumed, the flame is found to move closer to the droplet surface until the flame cannot sustain itself any more due to increasing scalar dissipation rates. Furthermore, results show that at very low temperatures typical of high-altitude relight conditions no flammable mixture is available around the droplet. Therefore, the success of an ignition event mainly depends on the energy released by the spark and the rate at which this energy is diffused toward the droplet surface to enhance the evaporation rate and create a flammable mixture. The findings are analysed from the perspective of gas turbine applications.