What are "Netzivim"?
Rashi: They are appointees to collect taxes.
Why does it say "va'Yasem Netzivim be'Edom b'Chol Edom Sam Netzivim"?
Radak: Verse 6 says that he put Netzivim in Aram, in Damesek. Do not think that also in Edom, he put Netzivim only in one place - therefore it says b'Chol Edom.
Malbim (13): David put Netzivim, and Edom rebelled, and he conquered all of Edom and put Netzivim in all of Edom.
It says above (verse 6) that Hashem saved David. Why is this repeated?
Malbim: David conquered Aram Naharayim (Surya) against the Halachah (Sifri Sof Ekev. We must conquer all of Eretz Yisrael before going to conquer out of Eretz Yisrael! This is called Kivush Yachid, like the Rambam says.) Even so, Hashem saved him. He foreshadowed the future, when He will add to Eretz Yisrael the lands of Kini, Kenizi and Kadmoni, i.e. Edom, Amon and Mo'av.
QUESTIONS ON RASHI
Rashi writes that the Netzivim were appointees to collect taxes. It says in Melachim I, 11:15 that Yo'av killed all the males!
Malbim (Melachim I, 11:15): Initially, David put Netzivim. Later, Edom rebelled, and they killed all the males 1 .
Perhaps they collected taxes from the females, or from other nations who came to live there after he called all men of Edom. (PF)
Here (verse 13), Malbim said that after Edom rebelled, David put Netzivim in all of Edom! (PF)