The provincial law or Provincial law. Sometimes the article is in front of provincial and other times no article.
The provincial law states that trade in ivory is prohibited.
Provincial law states that trade in ivory is prohibited.
The first sentence states that there is a singular provincial law and that it is prohibiting trade in ivory. There may be other categories of laws, but we are talking about provincial law.
The second states that there is a part of the Provincial law as a group noun (as a whole) that prohibits trade in ivory. Meaning that there are many laws that fall under "provincial law" and that one section of it bans ivory trade.
Which to use depends completely upon what you are trying to state.