(I posted the below message in February but the moderator never formally approved... I don't know why... anyway reposting it now as it may help you and hopefully will get published)
I had the same issue with my HP OfficeJet Pro 9015.
The cartridge carrier became stuck to the right and would not move either by the printer or manually. I followed this instruction and it helped:
But then like most of you here, I found out that a small plastic gear was broken (red point on the picture).
I did not even bother to contact HP customer service knowing I would only be wasting my time with them.
I spent ages trying to look for the same gear online or even something mildly similar. No luck!
I tried to glue with some cyanoacrylate glue the gear but the pressure is too high and it snapped again immediately.
I then made a CAD design of the piece as best as I could. This gear is really tiny! I was about to 3d print it but a friend of mine has a carving CNC machine (Carvey) and we ended up carving the gear out of a 3.2mm acrylic sheet. It is less than the 4.3mm thickness required for the gear but it was not a big deal as I ended up gluing two gears together. Thickness was not a real constraint here anyway (as long as I have enough space to put the gear on the axle). In fact, I think doubling it up has the added advantage of increasing the friction area and reducing stress on the piece. It also prevents the gear from moving too much on the axle. To ensure the piece held well, I also put a tiny amount of glue inside to fix it better to the axle.
So far so good, everything works... fingers crossed it will last!
(Happy to share the CAD file)