Every user is able to update an existing version of a published script. Please open your Pine editor and press the publish script button to do that. Make sure that your update is in the pine editor tab & is applied to the chart. When you have published scripts, they will show up in a drop-down menu. Choose the one you wish to update. You can adjust the description field and the style of the update (side by side or linear) and then press Publish New version to finish.
By default, the chart used when you update will replace the previous chart in your script's page. You can choose not to update your script page's chart, however.
If you do not want to update the publication's chart, so you check the "Don't update the chart" checkbox: