It depends!
Fixes for breaking bugs (say, the game can't be played on MacOS, or level doesn't load appropriately and so on) can be fixed and uploaded without ado.
If you have a major update, more content, changes in gameplay and such, a post-jam version is needed.
You do need to keep the jam version, but you may decide to publish it side by side. You may do so during the jam or after the jam, that's for you to decide, but you need to make clear which is the jam version and which isn't.
I have seen people suggest to upload the Post Jam version as a separate itch.io game, and keep the entry in it's own page (maybe linking to the post-jam version) that way the jam version will always be available and easy to find
Hope that helps!
For future reference: it really should be on a separate page. I accidentally uploaded the post jam build (which was almost entirely graphics/sound changes and a few level tweaks) to the same page and somehow managed to take down the old one in the process.
More info in this thread.
