Google tells me your the 4G Jetpack is a WiFi->4G device with no connectors for wired network.
That means the printer must be connected to the notebook with a network cable.
Using a switch between the notebook and the printer may or may not be required: if the link LEDs light up on both ends (and/or Windows reports that a network cable is connected) when a cable is connected directly from the notebook to the printer, you won't need the switch.
Your notebook will now be connected to two separate network segments: one will be the wired network segment, which will be very simple and basically only contain your printer. This segment should have no default gateway configured, since it has no connectivity to the outside world.
The other network segment will be the wireless network segment, which should remain auto-configured by DHCP, just as it is now.
First, you will need to find out the IP address your notebook is receiving from the 4G Jetpack.
Open the Command Prompt (click Start -> Run...,type "CMD" and press Enter), then type "ipconfig /all" and press Enter.
This will display all the current network parameters in a single listing.
There are three "private-use" IP address ranges that can be freely used by anyone:
A) 10.*.*.*
B) 172.[16..31].*.*
C) 192.168.*.*
If the IP address on the wireless network interface is in one of these ranges, you should choose one of the other ranges for your wired network segment.
(This is greatly simplified: if you understand IP addresses and netmasks, you might choose to use another subnet within the same private-use address range, if necessary.)
Since there is no device in your wired network segment that could work as a DHCP server, you must set static IP addresses to both the printer and your wired network interface.
Here are some example settings you could use:
For address range A:
- IP address 10.0.0.1 for the notebook's wired network interface
- IP address 10.0.0.2 for the printer
- Netmask 255.255.255.0 for both
For address range B:
- IP address 172.16.0.1 for the notebook's wired network interface
- IP address 172.16.0.2 for the printer
- Netmask 255.255.255.0 for both
For address range C:
- IP address 192.168.0.1 for the notebook's wired network interface
- IP address 192.168.0.2 for the printer
- Netmask 255.255.255.0 for both
If the printer will not accept the network settings without setting the default gateway, then use the address of the notebook's wired network interface as a gateway address for the printer.
In any case, leave the default gateway setting empty in the configuration of the notebook's wired NIC - this allows you to use the 4G jetpack to get online.
After you have the IP addresses configured, the next step is to set up the printer in Windows.
Start the Add Printer wizard. When it asks if you're adding a local printer or a network printer, choose Local (really; the "network printer" really means "a shared printer from another Windows system" here). Then choose "Create a new port". The type of the port to create should be "Standard TCP/IP printer port". You'll need to specify the IP address of the printer and the TCP port number (which is 9100 for HP JetDirect-compatible network printers). After that, just follow the instructions on screen: Windows might auto-detect the printer model, or might need you to specify it.