Rooted binary trees are often used to represent evolutionary processes such as speciation, divergence of populations, and coalescence of different genetic lineages to a common ancestor. However, to represent events of hybridization of biological entities, rooted phylogenetic networks are used. In the past few years, combinatorial properties of several biologically relevant classes of phylogenetic networks have been extensively studied. We study the simplest phylogenetic network – galled trees – where nodes can be in at most one reticulation cycle. Specifically, we look at time-consistent galled trees, equivalently normal galled trees, where the two hybridizing nodes and the reticulation node coexist when viewed as biological entities in time. In previous work, we found the asymptotic approximation of the number of unlabeled galled trees with given numbers of leaves and galls. Here, we find such asymptotic approximations for leaf-labeled galled trees with given numbers of leaves and galls. This work adds to the knowledge of asymptotic approximations of the number of networks in biologically relevant phylogenetic network classes with given numbers of leaves and galls. In particular, whereas the approximation for the number of general phylogenetic networks was found to be identical to the approximations of the numbers of networks in several more restricted phylogenetic network classes, the approximation for galled trees has a smaller value.