Let $r\ge 2$ and let $t_r(n)$ be the Turán number (the maximal number of edges in a graph on $n$ vertices with no $K_{r+1}$). If $G$ is a graph with $n$ vertices and $m\ge t_r(n)$ edges there exists a clique on $r$ vertices, say $x_1,\dots ,x_r$, such that$$d(x_1)+\cdots +d(x_r)\ge \frac{2rm}{n}.$$