After an adventure or two odds are your PCs have done something worth talking about. The exact story may not get out, but that a villain was defeated or a scheme was disrupted will get out and around. People will take those stories. They will embellish them. They will run with them and tell them all over the place. And by the time your PCs catch up with a version of their story they may not even recognize it.
But do you?
Running with the rumors and stories of a PCs deeds is not only a great way to have fun and show how things twist and disrupt over time, but can also put the PCs in fun situations where NPCs have expectations for them that they can't possibly match - for good or for ill.
So think of the outcome of your last adventure. How does the story of that spread? How do the bards and storytellers of your universe change it to 'be a better story'? How do you add drama, adventure, heroism, and villainy to it? Even if it already has those things in spades, people will still tweak and change things to suit their needs.
What do people where the PCs are next going know about it? How do they feel about it? Do people looking for a hero see this as their salvation? Or is it just another group of thugs coming to take what is theirs? Can the PCs change that view?
Have fun with it. let the PCs run into it. Let them enjoy the fame. Let the fame bring them to the attention of a bigger villain. And then have fun with that too.