A very warm welcome to the HP community. A very good day to you.
I understand that you have an HP Deskjet 895cse Printer and it does not print from a Win7 computer. I read that the printer works well with an older Win7 computer. I'll do my best to help you with this case.
It is purely something related to the drivers. The drivers for this printer are not available. However, I have a workaround using which the printer should print on the newer Win7 computer. I suggest you to refer to the below steps:
Search Windows for devices, and then click Devices and Printers in the list of results.
Click Add a printer.
Figure : Clicking Add a printer
Click Add a local printer.
Figure : Selecting Add a local printer
Select Use an existing port (USB001: Virtual printer port for USB), and then click Next.
Click Windows Update, and then wait for the print drivers to update.
Click HP, Hewlett-Packard, or Hewlett Packard in the Manufacturer pane, and then click the name of your printer in the Printers pane.
NOTE: In the list of the printer driver displayed, please select drivers for HP Deskjet 990c and continue with the installation.
7. Click Next, and then follow the on-screen instructions to install the driver.
8. Disconnect the printer USB cable from the computer, and then reconnect the cable. You can now use your printer.
Please refer to this link for more information about Installing and Using the Windows Built-in Print Driver
I hope this does the trick. Let me know. Good luck! 🙂