Set Default/Null Value with Select TagHelper

You can just insert an option item inside the select:

<select asp-for="Category" asp-items="@ViewBag.Category"  class="form-control">
    <option disabled selected>--- SELECT ---</option>
</select>

The disabled keyword in the code above means that the "--- SELECT ---" row cannot be picked again once a choice has been selected in the list. If you want the user to be able to blank the selection again (i.e. if it's bound to a nullable field) then just omit disabled.

If you want to store value null to database then use <option selected value="">Full Access</option>