I am working with a new designer who feels strongly that when you use a pencil icon signifying edit you must also add the text "Edit" next to the icon. This is not consistent with how our other pages were designed, we simply displayed the pencil icon. Is there a design standard?
Adding the label will likely only increase clarity.
However, you may find an answer I wrote only last week useful, which describes some qualities that a button should have in order to be understood more easily. In it, I mention that there are several aspects to consider, and consistency in design is one of them.
If you've established a pattern that your users are used to (i.e. using the pencil icon with no label), then being consistent in that way may be a defensible position. However, if you have the real estate for it, then it's generally a good practice to add labels to accompany your icons when possible and appropriate.