Catalyzes the phosphorylation of D-glycero-D-manno-heptose 7-phosphate at the C-1 position to selectively form D-glycero-beta-D-manno-heptose-1,7-bisphosphate. ATP + D-glycero-beta-D-manno-heptose 7-phosphate = ADP + D-glycero-beta-D-manno-heptose 1,7-bisphosphate + H(+) Nucleotide-sugar biosynthesis; ADP-L-glycero-beta-D-manno-heptose biosynthesis; ADP-L-glycero-beta-D-manno-heptose from D-glycero-beta-D-manno-heptose 7-phosphate: step 1/4. Bacterial outer membrane biogenesis; LPS core biosynthesis. Belongs to the carbohydrate kinase PfkB family.