There are several options here. I will divide them between the options directly in the book and the other options I have set for my players.
The party has some official means to get hold of a large sum of money at the beginning of the adventure.
Chapter 1 of Zhentarim Hideout contains a secret room. It contains 4 tables worth 75 gp each and 15 silver bars worth 50 gp each – for a total run of 1,050 gp.
In addition to that, there is …
A much smaller amount of hidden treasures in the Xanathar guild hideout, totaling 26gp.
This brings us closer to the amount needed simply with the treasure found. As for making a difference …
Istrid Horn, a Zhent, is listed as being available to offer loans of up to 2,500 in. At a rate of interest of 10% per payment (see introduction)
Some missions of the faction also pay …
The Emerald Enclave Level 3 mission pays 100 gp per participating character.
The Harpers Level 3 mission gives a spellbook with level 2 spells (see below, this may be worth money for Obaya)
Zhentarim's Level 2 mission pays 50 gp per participating character.
Zhentarim 3rd level mission pays 15pp (150gp) fixed rate
If you're thinking of linking to the mad mage's dungeon …
Obaya Uday offers gold for spellbooks, based on the book's highest fate. For a book containing only 1st level spells, such as the one that can be found in Xanathar's guild hangout, she offers 5pp (50gp). For level 2 spells, like the one from the Harpers Level 3 mission, it offers 25pp (250gp).
From there, these are all the extra options that I have offered to my players, while limiting them to the characters in the book (and some older information about them, in one case).
As for other sources of loan …
Mirt, Harpers is known as Mirt the Moneylender. He could probably be called to lend money to the party … and if a party member is recruited from the Harpers, he might well get them a good deal. The Cassalanters are also called as lenders, which could lead to some very interesting gameplay as they are also the bad guys. Finally, Appendix B gives the name of another family that serves as a lender: the Irlingstars. Annex B also indicates that Istrid's interest rates are in line with those of other lenders, so again … 10% by bank transfer (which is steep … ouch)
Beyond that, there is the option of sponsorship and investment …
Mirt is extremely rich … if the party can make it attractive, it could be persuaded to invest in catering for one percent of the profits. If you are proposing to make the manor a safe place / center of operations for the Harpers, it could simply cover your missing margin as an investment in the welfare of the Harpers. Any other noble that the party has come to know (like Raenar Neverember) could also be a possible investor. And, of course, any other faction could eventually sponsor the repair of the mansion as long as it would be beneficial to them.
Finally, although these options are available to my players, I gave them the opportunity to be creative. When it comes to buying money, players can be quite inventive. I nudged them to make sure they found all the loot hidden in Chapter 1, which really put them close to what they needed. So, I simply asked them where they were going to find the rest of the money.
One player started selling his services as a caster for a while and the Bard went on tour in the city.
The only hypothesis put forward in the rest of the adventure is that the PCs can be found at Trollskull Manor. This is the centerpiece of the Fireball event … because a person was addressing the mansion players when they were attacked. There is no assumption that this has been repaired or that he is back in business.
Thus, players can choose to renovate it now, renovate it later, or simply live indefinitely in a broken half-ruin.