I ran a long Night’s Black Agents campaign (hacked to PbtA) that involved a lot of chases. One thing I found helpful was breaking longer chases into distinct parts or legs (e.g., first leg of car chase through town to police roadblock gives way to second leg of offroad chase through the woods gives way to foot chase), and making sure they faced a variety of challenges or decisions. Some basic types to consider:
Reactive decisions: The most common thing to throw into a chase scene, but overuse can make things feel exhausting or repetitive. You take a few steps on the rope bridge and one of the support ropes just snaps, tipping the whole thing sideways. What do you do?
Navigational decisions: If it’s an epic chase, consider integrating one or more junctures where they have to choose between two routes, each with inherent temptations and drawbacks. From the ridgeline you’ve just topped, you can see the tower in the valley far below. The right slope is a massive scree, tumbling steeply toward a dark wood of broken fir trees; to the left the mountainside cuts down into a sheltered ravine, but to get there you’d have to cross a stretch of exposed rock. What do you do?
Team management decisions: Give them tough choices by threatening their followers or fellow PCs. A cry rings out, and you look back to see that Darcy took a spill at that last rotten log you crossed. He’s not back on his feet yet, and the big lizard is bearing down. What do you do?
As far as mechanical approaches, consider formalizing the chase with a move. For example (off the top of my head, so untested):
RUN FOR IT
When you lead a chase, set Quarry (that’s you) to 1, Pursuer (that’s them) to zero, and ask the GM to choose a Finish value from 3-7, depending on how far you need to go to reach the next juncture.
Then, go go go and roll +DEX: on a 10+, Quarry gains 2 and you describe how you outdistance your pursuer; on a 7-9, Quarry and Pursuer each gain 1, and they’re still on you when you look over your shoulder; on a 6-, you face an unexpected hazard, hard decision, or other problem of the GM’s choosing, which probably includes Pursuer gaining 1 on you.
When Pursuer equals or exceeds Quarry, they’ve caught up—you’ll have to deal with them somehow before you can do anything else. When Quarry equals or exceeds Finish, you’ve reached the next juncture, and the GM says what happens next.
In my own playstyle it’s super-important for failure on the part of the PCs to be a real possibility. If the PCs get captured or the opposition seizes the MacGuffin first, things can get really interesting in unanticipated ways. If you haven’t already done so, give some consideration to what a fail state would look like, and think about the implications, given the motivations and goals of all concerned.