Catalyzes the ATP-dependent dehydration of threonylcarbamoyladenosine at position 37 (t(6)A37) to form cyclic t(6)A37 (ct(6)A37) in tRNAs that read codons beginning with adenine. Displays only the t(6)A but not the ct(6)A modification in tRNAs. Unable to sustain respiratory growth under non-fermenting conditions. Present with 8430 molecules/cell in log phase SD medium. ct(6)A is involved in promoting decoding efficiency. It is an unstable modification that can be easily hydrolyzed and converted to t(6)A during nucleoside preparation by conventional methods (PubMed:23242255). Belongs to the HesA/MoeB/ThiF family.