How to turn Extract into syrup
Well, you can't really make "elderberry syrup" (as the term is usually understood) from only elderberry extract.  Fruit syrups are generally produced from a mixture of fresh berries, sugar, and water, which is cooked and then often strained.

You could perhaps make "elderberry-flavored" simple syrup by combining sugar and water, cooking it down to your desired consistency, and then adding some elderberry extract at the end once the syrup has been removed from the heat.  (Generally, you don't want to add extracts to liquids before cooking if you can add them afterward, since they often contain volatile flavor ingredients that could cook off and be lost.)  I can't specify proportions because extracts vary widely in terms of potency, so I'd add a bit of extract to your simple syrup and taste to see if it's something like what you want.

In any case, this result will be quite different from normal elderberry syrup that has actual fruit dissolved in it.  The flavor and consistency will be different.  However, depending on what you want to do with it, it could be useful.  (I would not use it on pancakes, for example.  But I might use it to provide a hint of berry to a mixed drink or something.)