how do you lot improve domain authority?

Worth remembering DA is Moz's score, not something Google uses, so chasing the number for its own sake is a bit pointless. It goes up for the same reason rankings do - links from sites that themselves get linked to. Make one or two things on your site that people would actually cite (original data, a genuinely useful tool, a definitive guide in a narrow topic) and pitch those. Bought links move the score and do nothing else.