Involved in thaumarchaeal hydroxypropionate/hydroxybutyrate (HP/HB) cycle, a modified version of the autotrophic HP/HB cycle of Crenarchaeota. Catalyzes the formation of 4-hydroxybutyryl-CoA, ADP and phosphate from 4-hydroxybutyrate, coenzyme A (CoA) and ATP. Can also use acetate, propionate and butyrate, with poor catalytic efficiency. 4-hydroxybutanoate + ATP + CoA = 4-hydroxybutanoyl-CoA + ADP + phosphate No activity with Ni(2+), Co(2+) and Ca(2+). In the N-terminal section; belongs to the acetate CoA ligase alpha subunit family. In the C-terminal section; belongs to the acetate CoA ligase beta subunit family.