This is a recurring pro-Kremlin disinformation narrative about NATO allegedly pursuing a belligerent and hostile agenda against Russia.
First, NATO is not encircling Russia. Russia's land border is just over 20,000 kilometres long. Of that, less than one-sixteenth (1,215 kilometres), is shared with NATO members. Russia has land borders with 14 countries. Only five of them are NATO members.
Then, NATO enlargement was not "contrary to promises". NATO Allies take decisions by consensus and these are recorded. There is no record of any such decision having been taken by NATO. Even if there was a personal assurance from an individual leader, it could not replace Alliance consensus and does not constitute a formal NATO agreement. This promise was never made, as confirmed by Mikhail Gorbachev, then-president of the Soviet Union:
"The topic of 'NATO expansion' was not discussed at all, and it wasn't brought up in those years. I say this with full responsibility. Not a single Eastern European country raised the issue, not even after the Warsaw Pact ceased to exist in 1991. Western leaders didn't bring it up either."
Central and Eastern European countries began seeking NATO membership in the early 1990s. NATO actively sought to create a cooperative environment that was conducive to enlargement while simultaneously building special relations with Russia.
Furthermore, NATO does not "expand" in the imperialistic sense as described by pro-Kremlin media. Rather, it considers the applications of candidate countries who want to join the alliance based on their own national will. As such, NATO enlargement is not directed against Russia. NATO's "Open Door Policy" is based on Article 10 of the Alliance's founding document, the North Atlantic Treaty (1949). The Treaty states that NATO membership is open to any "European state in a position to further the principles of this Treaty and to contribute to the security of the North Atlantic area". Every sovereign nation has the right to choose its own security arrangements.
See more similar disinfo cases alleging that NATO promised Russia it would not expand to the East and that NATO forgot all the previously existing agreements and expanded despite promises made to Gorbachev.