Once you have the exploit server up and running (Go here), updating the exploit version (HEN) is easy task.

For example, let's say we want to upgrade from HEN 1.6 (version that is already integrated with exploit server) to HEN 2.1

Steps:

1. Download new version of the exploit. (as reference, HERE it is for HEN 2.1)

2. Most of sources have two files in the exploit. E.g. index.html and ps4-hen-vtx.bin file.

        * See reference section down below for bin to html conversion link
   

3. Copy index.html file under /mnt/2G/ps4-exploit-host/exploits/5.05/HEN/

4. Copy ps4-hen-vtx.bin file under /mnt/2G/ps4-exploit-host/payloads

5. Reload exploit server (easiest way is to reboot your router)

After above steps, on your PS4 you should see HEN 2.1 when loading the exploit 5.05.

References:

New version of exploit is downloaded from following page: https://www.psxhax.com/threads/ps4hen-2-0-homebrew-enabler-for-ps4-5-05-via-sistr0.6790/

Direct link to HEN 2.1: https://github.com/SiSTR0/ps4-hen-vtx/releases/download/2.1/ps4-hen-vtx_5.05_v2.1_SiSTRo.7z

On topic of Bin to html conversion: https://www.psxhax.com/threads/convert-bin-into-index-html-for-5-05-exploit-and-payloads-guide.5505/page-4