watchOS 5.1.3 can be downloaded for free through the dedicated Apple Watch app on the iPhone by going to General --> Software Update. To install the new software, the Apple Watch needs to have at least 50 percent battery, it needs to be placed on a charger, and it needs to be in range of the iPhone.
watchOS 5.1.3 is a minor update that focuses on performance improvements and fixes for bugs discovered since the release of watchOS 5.1.2. We didn't find any changes during the watchOS 5.1.3 beta testing period. Apple's release notes do not mention any new features or include information beyond the general "this update includes improvements and bug fixes" statement.
The prior update watchOS update, watchOS 5.1.2, introduced the long-awaited ECG feature for the Apple Watch Series 4, allowing Apple Watch owners to take single-lead electrocardiograms to detect atrial fibrillation, which can be a sign of serious health problems.