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 (By similarity). Exhibits ATPase activity in vitro (PubMed:33412198). ATP + D-glycero-alpha-D-manno-heptose 7-phosphate = ADP + D-glycero-alpha-D-manno-heptose 1,7-bisphosphate + H(+) kcat is 104 min(-1) for ATPase activity. 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. Lipopolysaccharide biosynthesis; LPS oligosaccharide biosynthesis. Monomer. Belongs to the GHMP kinase family.