Microsoft continues to support Silverlight, and Silverlight out-of-browser apps can continue to use it. Silverlight will also continue to be supported in Internet Explorer 11, so sites continue to have Silverlight options in Windows 10. At the same time, we encourage companies that are using Silverlight for media to begin the transition to DASH/MSE/CENC/EME based designs and to follow a single, DRM-interoperable encoding work flow enabled by CENC. This represents the most broadly interoperable solution across browsers, platforms, content and devices going forward.
Considering that Windows 10 browser (Edge) will not support Silverlight, does ESRI have any plans for moving to other new technology?
Some links to check out....official sites
And to get started (disclaimer, my GeoNet blogs)
If you re a web developer Rebecca already mentioned that Esri provided options.
If you are a .NET developer then we have ArcGIS Runtime for .NET and we anticipate users from SIlverlight coming to this product. Take a look at the comprehensive doc which helps you to build native mapping apps for Windows desktops, Windows Phone, and Windows Store