My suggestion maybe seems a bit railroady...
...but your players won't necessarily know.
I DMed some chases (it was my home-brew system, but that issue is interchangeable)... and every time I started by writing an end for this situation or at least had some scenes in mind where it could be possible to catch the target.
The first chases I DMed were roll/skill-based... and that's just super tedious... it feels like Mensch ärgere dich nicht... I can't recommend to do that. It's just random and your players won't get the feeling that they can do much about it.
Rather give your players something to do and decide if they catch their target depending on how well they did that "something".
Here's an example
(Alert! That will be a longer story, but I try to keep it short):
The party was more or less stranded in a jungle after they escaped
from prison. They got in jail because of their former client. That
client was also responsible for the loss of their airship and they
were pretty much pissed about their soon to be frenemy. They were
pretty much low on supply and lived with and from the jungle for a few
weeks now. They had some encounters with local cults and even a
demigod called Samedi (yapp, like that Voodoo-Guy), wich was the big
bad of that part of the campaign... when they heard a steamboat (it
was a steampunk home-brew world) crossing the stream where they
camped. On board were some men in sailor uniforms aaaaaand their
former client. They had a little argument about money he owned to
them... let alone the costs of their ship... and the reward for their
last quest... and their arrest... etc. It was a pretty heated
discussion and I almost thought, that this guy is pretty much dead.
But I counted on my greedy players... and it worked out. He had this
sailor guys hired for his dangerous expedition to recover a very
valuable McGuffin and his boss will pay good money for that... they
won't get only the reward from their former quest and a part of the
reward for this quest... no, his boss will get them a new shiny
airship. They were stranded anyways... so they pretty much fell for
it. And it came how it had to come: The client screwed them again and
left them in a trap room while he stole himself away (with the
McGuffin of course). When they finally made it out, that jerk was far
ahead. He stole the steamboat and abandoned his crew... again. One of
the party's casters recently learned a spell that allowed exceptional
fast travel, but through the shadows... it was pretty much my
equivalent of the Border Ethereal, but more like Warhammer 40k's
warp space. And this part of the shadows was controlled by that
demigod the party ran into before... so they were trapped in his
labyrinth, had a few quests to do to prepare for a huge boss fight,
killed the demigod, left the shadows just in time (they did it
exceptionally fast), catched their former completely surprised client
and tied him up. They didn't kill him yet... because they still wanted
their money... so he had the opportunity to screw them a third and
last time. He ended up in a volcano shortly afterwards... but that's a
story for another day.
Before that campaign I had a investigation/puzzle chase... pretty much the whole campaign was a huge chase after an OP-Mary-Sue(ish) shape-changer assassin pumped up with magic items and combat drugs.
It all began with some murders that led the party onto her trail.
After a few encounters with this crazily overpowered enemy, they found
out that she was looking for some kind of weapon or device that is
able to focus the power of dead gods and do... stuff with it... I
don't want to explain to much... so this should be enough for you to
know at this point. I didn't know yet how they would end up in the
show-down scene, but I already knew where that battle would be: On the
deck of the McGuffin that happened to be an earth-dragon-ship that was
able to phase through solid material. Dragon ships were also a thing
in my world... Dragons were extinct elementals and their bones were
used to build ships that inherented parts of their elemental power.
Because of their phasing abilities it was exceptionally difficult to
get some earth dragon bones... so that ship was kinda special or to be
more honest the only one of its kind and it was deeply hidden under
the city that campaign played in. But I digress... It was pretty much
a scavenger hunt, stuffed with puzzles and hindrances, one dynamite
infused prison break, a journey almost halfway around the world, some
almost lethal encounters with Mary Sue (I didn't know it better back
then) and a hidden invasion clock ticking behind my DM screen. Because
everything Mary Sue was doing was preparation for their bosses to
invade the party's home city. When they finally found the McGuffin and
started its engines to meet up with McGuffin person (that was an
elemental being entitled to restore balance to the world by using the
ship's energy... blablabla... again: I was a much worse DM back
then^^). They had their fight, now leveled enough to prevail while the
battle for the city was raging.
Long story short: Think those situations backwards. From a possible key scene in reverse to your party's actions. At least that worked out in the past for me.
And a third rather short example that's pretty much how you should NOT do it... because it's TEDIOUS!
I had that Cthulhu Campaign in which my party was a mafia gang. They
had that heist, where they got screwed by their partners (yapp, I like that trope) and chased
after them. The following car chase were opposing driver checks. So I
rolled, they rolled, they got closer, their opponents got further
away, they tried to shoot the tires... it was just forgettable and
didn't create any memorable situations. Because I didn't plan anything and trusted the randomness.
The problem with the last example: You give away control where you don't need to do that and that leads very often into very awkward situations where you wanted to create a Hollywood blockbuster action scene. It can get very funny if you trust your and your party's story to random factors.
Another big but more general tip: Don't let randomness decide whether your party prevails in their story or not. Let it rather depend on how fast/creative/efficient your party solves the hindrances you throw at them... at least, when it comes to off-combat situations. Let it be a battle for creativity rather than for pure randomness.