Catalyzes the phosphorylation of D-glycero-alpha-D-manno-heptose 7-phosphate at the C-1 position to form D-glycero-alpha-D-manno-heptose 1,7-bisphosphate. ATP + D-glycero-alpha-D-manno-heptose 7-phosphate = ADP + D-glycero-alpha-D-manno-heptose 1,7-bisphosphate + H(+) Nucleotide-sugar biosynthesis; GDP-D-glycero-alpha-D-manno-heptose biosynthesis; GDP-D-glycero-alpha-D-manno-heptose from D-glycero-alpha-D-manno-heptose 7-phosphate: step 1/3. Cell surface structure biogenesis; S-layer biogenesis. Belongs to the GHMP kinase family.