As the fight for Mosul intensifies, different national interests are beginning to diverge. The fast PMU advance towards Telafar, the Iraqi Turkmen town in northern Iraq, Turkey is becoming very concerned and is even threatening a major intervention of its own, building up forces just across the border. In the meantime, the US military declared its intentions to launch an offensive on Raqqa soon, a move which is threatening both the Turks and the Russians. The former does not want to empower the Syrian Kurds, the latter wants to keep Syria whole.
Therefore, an opportunity has begun to open for the Russians, whose main strategic imperative is to force the breakup of NATO and European institutions. Because Russian and Turkish interests are beginning to merge (as the US largely ignores the concerns of its Turkish ally), Russia will begin a new offensive to try to split the US from Turkey. The propaganda campaign began long ago, but it will now intensify.
Meanwhile, the Turks and Russians will intensify military coordination, which has already been strengthening, as seen by the Turkish intervention in Syria late August. Russia could easily shoot down any Turkish plane flying over Syrian airspace, but it chose not to because it understands that a US-Turkey split is in the works. Indeed, the Turkish general staff has been meeting with its Russian counterpart, an unusual move for a NATO member state.
Russia may encourage the Turks to make a new intervention into Iraq, using its leverage with Iran to allow this. The Iranian-backed PMU could be halted from attacking the Turks, while the Turks use their already-good relations with the Peshmerga to march through their territory. Baghdad and the US will be kept out of this and this will no doubt enrage both sides in this possible scenario.
Russia could even encourage the Turks to begin an Arab uprising against the SDF in Tell Abyad, which will damage any US attempt to march on Raqqa. Any such attempt would be limited however, as the Turks do not want to get too involved in the Syria conflict. Nevertheless, Russia has realized the weak-points in NATO relations and will no doubt try to exploit them.