You mean the FSB? Or the GRU?
I assumed PJT was using the term KGB as a shorthand for Russian Intelligence, so I went with it, too, not wanting to disrupt the flow with a discussion of the exact TLAs.
The GRU, formerly Soviet Military Intelligence, lives on as Russian Military Intelligence. It was the Army then. It is the Army now.
As for the KGB, it lives on as the SVR (MI6/CIA/NSA — foreign spying) and the FSB (MI5/FBI — counterintelligence and domestic spying).
"Viktor Suvorov," a GRU officer who defected to the UK in the 1980s, wrote an interesting commentary on how checks and balances worked to preserve the Soviet regime. Excerpt:
A triangle is the strongest and most rigid geometric figure. If the planks of a door which you have knocked together begin to warp, nail another plank diagonally across them. This will divide your rectangular construction into two triangles and the door will then have the necessary stability.
The triangle has been used in engineering for a very long time. Look at the Eiffel tower, at the metal framework of the airship Hindenburg, or just at any railway bridge, and you will see that each of these is an amalgamation of thousands of triangles, which give the structure rigidity and stability.
The triangle is strong and stable, not only in engineering but in politics, too. Political systems based on division of power and on the interplay of three balancing forces have been the most stable throughout history. These are the principles upon which the Union of Soviet Socialist Republics is built.
...
Only three forces are active in the Soviet political arena-the Party, the Army and the KGB. Each of these possesses enormous power, but this is exceeded by the combined strength of the other two. Each has its own secret organisation, which is capable of reaching into hostile countries and monitoring developments there. The Party has its Control Commission-a secret organisation which has almost as much influence inside the country as the KGB. The KGB is a grouping of many different secret departments, some of which keep an eye on the Party. The Army has its own secret service-the GRU-the most effective military intelligence service in the world.
Each of these three forces is hostile to the others and has certain, not unreasonable pretensions to absolute power but its initiatives will always fail in the face of the combined opposition of the other two.
...
Let us look at an example of the way this triangle of power functions. Stalin died in 1953. Observers concluded unanimously that Beriya would take command-Beriya the chief inquisitor and head policeman. Who else was there? Beriya, his gang of ruffians, and the whole of his organisation realised that their chance to lead had arrived. The power in their hands was unbelievable. There was a special file on every senior party functionary and every general and there would be no difficulty in putting any one of them before a firing squad. It was this very power which destroyed Beriya. Both the Army and the Party understood their predicament. This brought them together and together they cut off the head of the chief executioner. The most powerful members of the security apparatus came to unpleasant ends and their whole machine of oppression was held up to public ridicule. The propaganda organisation of the Party worked overtime to explain to the country the crimes of Stalin and of his whole security apparatus.
...
Representing, as it does, a fusion of three powers, the Politburo is fully aware that it draws its own stability from each of these sources. It can be compared to the seat of a three-legged stool. If one of the legs is longer than the others, the stool will fall over. The same will happen if one of the legs is shorter than the others. For their own safety, therefore, the members of the Politburo, whether they come from the Party, the KGB or the Army, do everything they can to maintain equilibrium. The secret of Brezhnev's survival lies in his skill in keeping the balance between the trio, restraining any two from combining against the third.
That's how it worked then.
As for now, it looks more or less what a Mafia takeover of the US federal government might look.