If you install easy-theme-and-plugins-update from Wordpress, you don't need to delete the old plugin:
https://wordpress.org/plugins/easy-theme-and-plugin-upgrades/
WordPress has a built-in feature to install themes and plugins by supplying a zip file. Unfortunately, you cannot upgrade a theme or plugin using the same process. Instead, WordPress will say “destination already exists” when trying to upgrade using a zip file and will fail to upgrade the theme or plugin. Easy Theme and Plugin Upgrades fixes this limitation in WordPress by automatically upgrading the theme or plugin if it already exists.
In the case of themes, you MUST use a child theme. If you do not and update your theme, all your customisations will be deleted.
Good luck!