Is there a way to NOT allow a task or story to be closed if there's time remaining?

[MinB]

if there is still time left on a task or story, the user should not be allowed to close the task/story.

is there a way to do this? or is an add-on required?

[M]

You could also use the Workflow Toolbox to check the remaining estimate value. Here's a similar example in the plugin docs.

[Deniz Oğuz - The Starware]

You can write a script validator and attach it to close transition.  You can use ScriptRunner plugin if you want.