Topical authority is a fancy term for a simple idea: search engines trust sites that clearly know their subject. You earn that trust by covering a topic thoroughly, not by publishing scattered posts that never connect.
The practical move is to build clusters. Pick a broad topic, write a strong central page on it, then surround it with focused articles on the subtopics and link them all together. Each piece makes the others stronger.
Do this for a few core topics rather than chasing every keyword, and you become the kind of source both search engines and readers come back to.