This article reports measurements characterizing the Underlying Event (UE) associated with hard scatterings at midrapidity (|η| < 0.8) in pp collisions at s = 13 TeV. The hard scatterings are identified by the leading particle, the charged particle with the highest transverse momentum (pTleading) in the event. Charged-particle number-densities and summed transverse-momentum densities are measured in different azimuthal regions defined with respect to the leading particle direction: Toward, Transverse, and Away. The Toward and Away regions contain the fragmentation products of the hard scatterings in addition to the UE contribution, whereas particles in the Transverse region are expected to originate predominantly from the UE. The study is performed as a function of pTleading with three different pT thresholds for the associated particles, pTtrack > 0.15, 0.5, and 1.0 GeV/c. The charged-particle density in the Transverse region rises steeply for low values of pTleading and reaches a plateau. The results confirm the trend that the charged-particle density in the Transverse region shows a stronger increase with s than the inclusive charged-particle density at midrapidity. The UE activity is increased by approximately 20% when going from 7 TeV to 13 TeV pp collisions. The plateau in the Transverse region (5