First thing most important please keep a full backup before doing any update.
Then you can do in this way:
If you have done all customization coding for your website in child theme and didn’t customize parent theme then you can download theme updated version and can upload (parent theme) to your hosting themes folder using ftp which will replace old themes files.
But if you have customize parent theme coding for your website requirements then if you upload updated theme then all your customization work will be gone.
Another way you can request to theme author to assist you how to proceed. contact theme author or post a commnets in theme comments page and let them know. Theme Author will assist you.