Turkish President Recep Tayyip Erdogan, in a speech to fellow party members in Sakarya, promised to “revise the outcome of World War I and annex Syrian territories (formerly Ottoman provinces) into Turkey,” Telegram channel “Turkey’s Top News” reported.
It goes against the idea of NATO which is based off the United Nations Charter.
NATO is a defensive alliance where the respect for sovereignty and mutual defense is what makes it work.
Turkey going for annexation goes against the ideology of NATO by not respecting international sovereignty. NATO will never help them in a forceful annexation. But if everybody involved allows the annexation peacefully, eventually it will be accepted.
If Turkey annexes by force, there are 3 most likely possibilities: NATO kicks them out, NATO stays neutral and does not help (even when the Kurds/Syrians retaliate), or NATO keeps a defensive role at the border while ensuring humanitarian aid to the area.
Whether or not NATO recognizes the annexation will depend on a vote by the members (Most likely with a high approval requirement).