During the World War I, what promise did Great Britain make to former Ottoman Arab provinces about their status after the war?

Sykes-Picot agreement

Arab region under the Ottoman Empire would be divided.

Explanation:

More than a year after the agreement with Russia, Great Britain and France also signed a secret agreement known as the Sykes-Picot agreement, by which most of the Arab region under the Ottoman Empire would be divided into British and French spheres of influence after World War I.

As for Iraq itself, Sykes-Picot did not guarantee the creation of the Iraqi state: separate negotiations with Arab leaders like Faysal led to that mess. It did, however, establish that the territory that would be known as Iraq was under British authority.

The Sykes-Picot Agreement created the modern Middle East. ... The line across a map of the Middle East it drew created colonial spheres of influence that cut directly and artificially across a region that had previously been divided along ethnic, linguistic and religious lines

by creating a labor shortage that pushed the continent toward a market economy