Thank you for the information.
From a purely technical standpoint there are ways to solve this. However, other limitations apply. Universities, other educational institutions, hospitals, authorities, companies, et cetera, need to restrict access to information in networks. So, as Allan Jones also pointed out, you would have to ask your IT department for advice about what or what not to do.
So, the following is only based upon what a normal user could do at home.
An HP ENVY 5530 printer would work with AirPrint and/or via the HP Smart app mentioned by sberman. However, that would require access to a Wi-Fi network. The iPad Pro and the HP printer must be connected to the same Wi-Fi network.
If it is not allowed, or appropriate, to engage an existing (Wi-Fi) network at all in (AirPrint) printing, one could establish another, separate, private Wi-Fi network for printing purposes only. The easiest way would be to use almost any simple/used Wi-Fi router without connecting its WAN port to the Internet. That is, only the local (LAN) side of this router would be used. If the iPad Pro is a cellular/mobile model, access to the Internet could be provided that way. Alternatively, a mobile broadband router (with a LAN/Wi-Fi section) could be used.
The HP ENVY 5530 would per se make it possible to connect directly from a computer/device to the printer in a Wi-Fi direct mode (where the printer itself provides a Wi-Fi network), but the router method (infrastructure mode) is often better.