Extend existing exterior outlet for grill island
On its face the idea seems reasonable. I suppose that at some point an outdoor kitchen would require the same kinds of things an indoor kitchen does (two small appliance outlet circuits, for instance). But if your grill island doesn't end up looking like a kitchen, it's probably reasonable to claim that an outlet attached to it is for landscape or general use and add it to the existing outdoor outlet circuit as you described.
There are many details to be attended, such as type of conduit, the depth it is buried, the type of wire or cable used, GFCI and possibly AFCI protection, and so on. But those are more relevant to &quot;how can it be done?&quot; and apply more or less the same regardless of whether or not a new circuit is added.