  Generalized Tur\'an problems ask for the maximum number of copies of a graph
$H$ in an $n$-vertex, $F$-free graph, denoted by ex$(n,H,F)$. We show how to
extend the new, localized approach of Brada\v{c}, Malec, and Tompkins to
generalized Tur\'{a}n problems. We weight the copies of $H$ (typically taking
$H=K_t$), instead of the edges, based on the size of the largest clique, path,
or star containing the vertices of the copy of $H$, and in each case prove a
tight upper bound on the sum of the weights. A consequence of our new localized
theorems is an asymptotic determination of ex$(n,H,K_{1,r})$ for every $H$
having at least one dominating vertex and mex$(m,H,K_{1,r})$ for every $H$
having at least two dominating vertices.
