There is no mention of NATO in the opening titles, and Drake indicates he is working for the American intelligence services (using the phrase "our embassy" at one point), much as he did early in the series (ie. Josetta (1960)).
The piano piece that Shumak plays at the concert and later (twice), for the president is Chopin's Etudes Opus 10 #12, the "Revolutionary". As it lasts a little over 2'30", presumably he played it again as an encore at the end of the concert.