Well, if you look at the old Cold War era James Bond movies, 007 doesn't actually fight the Soviets that often. In fact, more often than not, the KGB is more like a 'worthy rival' or even 'anti-hero allies' instead of outright being the antagonists. Take for example the head of the KGB in the series, General Gogol: In all the movies that he showed up in he was alway polite towards both M and Bond, at one point, even stopped his bodyguard from shooting the latter when he stopped the KGB from getting their hands on a British decryption machine. Or Anya/XXX, the female KGB agent in "The Spy Who Loved Me", who was for the most part a co-hero alongside 007.
So for TTL, I am guessing that the KGB will take the place of SPECTRE as the main villain for the most part. And once the USSR collapses, you will see a lot of the Bond Villains and the Henchman having former KGB/Red Army officer/Communist terrorist as part of their background.