Every n-vertex 7-connected 1-planar graph has at most 4n-12 edges, 4n-16 triangles, n-6 copies of K4, and thus at most 10n-33 cliques total.
Wood, On the maximum number of cliques in a graph,Graphs Combin.23(2007), 337–352
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The maximum number of $k$-cliques of 7-connected 1-planar graphs
Every n-vertex 7-connected 1-planar graph has at most 4n-12 edges, 4n-16 triangles, n-6 copies of K4, and thus at most 10n-33 cliques total.