You can buy complete panels or individual slats to fit between existing fence posts. Concrete posts usually have slots so the panels / slats can simply be lowered into them. There are a variety of ways to construct a fence with wooden posts, depends upon what you already have, how strong it needs to be, and what appearance you want. When you say "no slots" do you mean the existing fence posts are simply square faced, with no channels or fixtures? What are the posts made of, wood or concrete?
Measure the distance between each of the posts, and their height, then check if these dimensions match those of any ready-made panels from DIY / building suppliers. Some panels are pretty flimsy, so take into account how exposed your garden is and how windy it can get. Consider how and why the fence degraded last time. The best way to protect it from rain damage is with exterior paint. Not only is this the most durable defence, but signs of eventual wear will be obvious, providing a visual cue for renewal.