DS9 featured continuing storylines, and there was the story arc of when the Dominion took over DS9 in season 6 that could be considered such an arc. But DS9 still felt more episodic otherwise. You could watch most episodes without seeing the preceding episodes and not be adrift. I think the 3rd season of Enterprise was Star Trek's first attempts at a season long arc though--and that fed into season 4, just on a smaller scale with 2 or 3 episode arcs. But like most things in the entertainment industry, someone didn't just turn on a switch and create series/season wide arcs like are common today. It was a gradual shifting. DS9 could be considered an early flirtation with less episodic Star Trek. Even going to TNG, they did feature characters and story elements that cropped up later. And their was a loose gradual story from the first episode to the last. DS9 too it another step, as did Voyager. Enterprise was another step and Discovery now moved us more in line with what's currently popular.