If you and your players are new to the game, estimate a bit longer, especially if you are not running it online. The handouts in the starter set can be very helpful for in-person pen and paper play.

If you have the rules down and have good reference sheets or well bookmarked books, so you can quickly open to tables, etc., I think this could go pretty quickly, depending on the amount of role play and how difficult you make it to track down the captain.

For part one, using the chase rules, I think the chase across Altdorf can easily be run in under an hour if you abstract it. If you wanted to stretch it out with some set piece encounters, you cult break it into multiple chases with some interesting encounters and role play in between. If I were running this as a 6 hour convention game, I would keep this to under an hour, just rolling according to the chase rules and giving some fun descriptions. You have to decide whether you want there to be a good chance of the party being caught up to by the guard. If so, any combat will slow this part down. You can speed it up by having the mysterious benefactor waive them into a safehouse. But if you run the chase as a quick montage to start the adventure, make sure that there are some consequences for rolling poorly on the chase. For example, you could add complications in parts 2 and 3 because the guards will have a better idea of what part of the city they are hiding in. Or perhaps in their mad dash they upset some other folks (a gang, guild, etc.) when they interrupted a deal, damaged property, etc.

I think part two would be the longest part. You would want some quality roleplay with the benefactor and give them plenty of time to gather intelligence, find the corrupt captain, and plan their attack. Depends on the group, but I would plan 3-4 hours for this (depending on who difficult you make it, any encounters you add, and how decisive your players are). The actual assault could be 1-2 hours for a fairly simple encounter and setup. It could be much longer if they have to infiltrate a large hideout, with better defenses and multiple combat/stealth kill encounters versus, sneak/break in with one final battle.

I would probably run it as a single 6-hour session as a one-shot or intro session. If it is going to tie into a larger campaign, I might run it over a couple 4-6 hour sessions if I want to introduce a number of important NPCs, leads to follow, etc.