I'm running D&D these days, but in another game I ran years ago that wasn't D&D, I had large amounts of time between stories. Once as long as seven years, but usually between 6 and 24 months. Players in that game had a lot of fun working with me, playing out scene, advancing their characters' lives. Lots of meta and OOC, lots of side sessions. These days, not a lot of players seem to want to take me up on that.
In the game I am running now, I narrate the existence of downtime, and then ask if anyone wants to do anything during that. I try to invite time for personal growth, but not everyone has the time so I don't make it a requirement, nor do I run sides where people can level up past the group average. It's all character development stuff. I make myself available for side sessions, or for PCs to chase down their own leads.
I also narrate several "Here's something that happens in the next few days if anyone wants to address or react to it." If no-one wants to react to it, then I develop it, and it will come up later. One of those is just hitting now, from a lead they ignored six months ago.