Yes, your Duke of Edinburgh's (DoE) Gold Award will automatically count towards your King’s Scout Award (KSA), in place of the 5 KSA challenges.
The awards are closely linked. If you’ve completed your DofE Gold, there are just a few more requirements you’ll need to complete to achieve your KSA.
You can find more information in the Adventure Begins leaflet.
This leaflet is also available to order from Scout Store.