Updating Packages

I have a policy for the software, nothing is checked for trigger, the execution frequency is set to ongoing and the scope is for all computers.

You will have to have some kind of trigger for it to execute. Just having it set to Ongoing and scoped to all computers isn't enough. No trigger means it will never get run. Unless it's using a custom event trigger and that trigger is being called from something else, like a script running in a different policy.
To be honest though, I'd probably not use a scope of all computers, but rather would look at using a smart group. For example, a group of machines with the software not installed, or having an older version installed. This can be done using the built in Patch Management titles, assuming its something Jamf currently tracks. Or as a "traditional" Smart Computer Group that uses Application Title and Application Version criteria for starters.

Finally, if you set any trigger to it and choose not to change the scope, you will likely want to change the execution frequency from Ongoing to something else since that would mean it will install every time the trigger runs. If you set it to, for example, recurring check-in, then every time any Mac checks in it will run the installation, again and again and again, endlessly. Definitely NOT want you want to happen. However, that scenario can be avoided if using a Smart Group properly as the scope, and the policy is collecting inventory on completion.

So if I set the trigger to login and the execution frequency to once per computer, when I update the package will it notice that it is a new version and install automatically? Or will I have to create a new policy for the updated package?

That depends on how the policy was set up. If it has always been set to a trigger of “none” and a frequency of “ongoing” then it may never have run on any Macs. But to be sure you need to look at the policy logs. You see, when talking about the once per computer execution frequency, the policy logs are the main way the Jamf server knows if that policy should run on a Mac again. If there’s a policy log (success or fail) for any given Mac, then it considers that to be its “once” execution and it won’t run again on that machine. The way to fix that is to flush the policy log for that machine. So in essence, if you want to ensure the policy will run again on all scopes Macs, flush the entire policy log. That will make it appear like a new policy to those Macs. I normally don’t recommend flushing a whole policy log, but in this case that may be your best bet.

@bmichael Don't forget to check out JAMFs training programs and other such documentation! They're awesome!