Mr. Wilson, the Russians, or the Russians acting for Mr. Wilson?
The traitor was not killed: it was Edward's son. But he was going to marry a "former" Soviet spy, and Edward knew that espionage world is full of lies and tricks, and feared that "Ulysses" hint at the fact the Soviets could not trust her was, in fact, an attempt to plant a Soviet mole inside Edward's family. So... Edward was possibly the one who gave the order.
Actually, the implication of the final meeting with Ulysses suggests that the Russians had the woman killed, at Edward's request. In that scene, Edward declines to work with Ulysses. However, Ulysses replies that there will come a time in the future when he may seek a favor from Edward. He then abruptly changes topics to discuss the fact that this woman, whom he earlier noted can be trusted by neither side, is about to join Edward's family. And doesn't Edward want her to join his family? He does not reply.
However, later, Ulysses's Russian companion asks if he can borrow a dollar to make a purchase. Edward hands him a single dollar bill, and then says that it would be a cardinal sin to not be generous.
At the very beginning of the film, you'll remember that a small boy hands a bill to Edward on the bus. The serial number is later checked against a list--an agent named 'Cardinal' is sending a message to CIA. (In Tom Clancy's novel _The Cardinal of the Kremlin_, 'Cardinal' is the code-name for the CIA's most high-placed agent in the Kremlin.)
One implication is that with the simple exchange shown, Ulysses and Edward agree to the following exchange--the KGB will kill the woman in exchange for information regarding a high-placed CIA asset inside the Soviet Union. Alternatively it could be interpreted that actually Ulysees' companion IS Cardinal and that asking Edward for a dollar is his way of saying that he has information he wishes to provide, their remarks to one another and the use of the term 'Cardinal' a pre-arranged code. Possibly this information is concerning Edward's son's lover who Edward is then able to kill as a result.
Actually, the statement being made is that "assets" like the woman in Africa are fungible accounting units, to be discarded at will. Much like the way the former Yale professor was casually killed in London. The question of who "gave the order" is a trivial
accounting concept. The process killed the woman, the way the process disposes of other individuals who are just visiting while the various Bonesmen keep the wars small.
Edward's son was not a traitor. He was the chump caught in a Soviet honey pot. This is one
of the workhorse ideas of cold war lore - the russians taking advantage of the recurrent american inability to keep it in their pants. The rather broad assertion being made is that Edward's father fell in the same way, Edward himself got involved in Berlin, and therefore Edward's son was ripe for the plucking.