There’s no built-in modpack update function because there is similarly no modpack installation function. The Store, which is in beta, just downloads a modpack’s server files and unzips them into your directory.
Your best bet for updating a modpack would be to download the new version, backup your old server, then replace at least the mods and configs folder with the new pack’s mods and configs folder.
When in doubt, refer to the Modded Minecraft guide. It’s for first time setup, but it could still be helpful. Just remember to always have a backup before attempting anything destructive like this.