Hi,
Just verifying that it is the hinge that has broken and not the hinge mount in either the display back cover or the base enclosure?
Here’s the [http://h10032.www1.hp.com/ctg/Manual/c04825536|maintenance and service guide] for the laptop.
I realize that it says for models 13-s000 through 13-s099, which doesn’t include your model number, but it was linked from this [https://support.hp.com/ca-en/product/hp-pavilion-13-s100-x360-convertible-pc/8499316/model/9259076/manuals|webpage] so presumably it applies to it as well. Also I can’t find any other guide that mentions model ranges with your model number included
Go to p.41 to view the necessary pre-requisite steps and then the procedure to remove the display assembly. This will give access to the hinges.
If the hinges are faulty then on p.18 item #2 you will find the part number for the hinge kit. If you search online using ''only the part number'' you will get results for suppliers.
If the problem is actually a broken hinge mount in the display back cover the part number is Item #8 on p.19 or if it is the hinge mount on the base enclosure it is item #16 on p.17. To replace the base enclosure you would have to nearly completely dis-assemble the laptop.
Hopefully this is of some help.