Old HP Printer connected to ethernet port on Nighthawk AX4300

> [...] Nighthawk AX4300 [...]

   "AX4300" is a speed, not a model number.  Look for "Model" on the
product label.  "RAX45", perhaps?

> [...] I can't get it to work on the Nighthawk. [...]

   "can't" is not a useful problem description.  It does not say what
you did.  It does not say what happened when you did it.  As usual,
showing actual actions (commands) with their actual results (error
messages, LED indicators, ...) can be more helpful than vague
descriptions or interpretations.

   I assume that there are some (invisible but) relevant LED indicators
on the router and the printer.

   Does the printer get an IP address from the router using DHCP, or was
it configured with some static IP parameters which worked with your
(unspecified) "my previous router" but are unsuitable with the new one?

   Visit http://netgear.com/support , put in your (actual) model number,
and look for Documentation.  Get the User Manual (at least).  Read.
Look for "Address Reservation".

   Which kind of "not work" is this?  If your (unspecified) computer is
expecting to find this printer at some particular IP address, and you
didn't reserve that address for it on the new router, then your
(unspecified) computer might have trouble communicating with it at its
new/different address.  As usual, many things are possible.

   When all else fails, there's always the old reliable:

      https://en.wikipedia.org/wiki/RTFM

   Visit hp.com, put in your model number, get some documentation, and
read and follow the printer set-up instructions.