There is no mechanism in NATO to evict a member and no sign that Turkey wishes to leave. The base case is Turkey stays in, with increasing tensions for the time being over policy and what can be shared and done together. The more Turkey cosies up to Russia, the less likely the US will share technology and secrets with Turkey. NATO is not about to turn against the Kurds that have helped it in Syria, though no-one seems to have a solution to the Kurdish problems.
Syria is likely to complete its brutal re conquest of the country with Russian help. There will be countless displaced people in Idlib seeking a new home. Turkey will have to decide how many and whom it might help, and look to its border defences if it wishes to say No to large numbers whose natural exit from Syria will be across the Turkish border. The EU will want to keep its arrangement with Turkey going that refugees stay in Turkey and do not travel on to EU members on the continent. This means the EU may well have to offer more financial and other assistance to Turkey to handle her border issues and look after refugees.
The EU has already provided substantial sums to help Turkey build a 911km wall with a height of 3m, with barbed wire at the top. The EU supplied some of the surveillance technology and military vehicles to enforce the border ban on people crossing from Syria. Presumably the EU and Turkey will use this tough border to make it difficult for refugees to flee Idlib into Turkey, with more deaths in Syria the likely result.
Turkey will continue to negotiate with Russia, who will generally wish to encourage Turkey to destabilise the eastern end NATO. Russia, however, will not agree with Turkey’s wish to have a buffer zone in northern Syria. It will be easy for Russia to appear as a better friend to Turkey than the USA all the time President Trump is waging what President Erdogan calls economic war against him.
The USA will want to keep inner NATO secrets from their formal ally. The President seems determined to pursue his trade war with Turkey which will drive Turkey further from the Western alliance. It will be another case where the US pattern of alliances and interests will diverge from the EU’s.
The EU is in the most vulnerable position. Their Association Agreement with Turkey makes Turkish policy of considerable interest to the EU. The current drift of Turkish policy is not the one the EU intended, as they sought to bind Turkey more firmly into western ways. The EU’s Association Agreements are contentious items. The one with Ukraine lay behind the secession of Crimea, where Russia was able to exploit the tensions caused by the EU policy within the former Ukraine.The Turkish one is not going to lead to a splitting up of the country, but it could lead to an important rift between the West and Turkey. The EU in its March 2016 Agreement offered Euro 3bn to Turkey in return for her keeping the migrants and not allowing them passage to the EU. The EU helped finance and strengthen the border fences which will mark the limit of Assad’s reconquest of Syria by force.