Nimitz gave Halsey perhaps the two toughest mission of the Pacific War: The Doolittle Raid and the defense of Guadalcanal when the issue was truly in doubt. His trust was amply repaid. In the Solomons Halsey bloodied the Japanese Navy, held Guadalcanal, and began the long advance toward Tokyo Bay.
Chester Nimitz and William Halsey were as different as two admirals could be. Nimitz was a submariner while Halsey was a carrier commander AND a carrier pilot. Where Nimitz was quiet and outwardly serene even in moments of intense stress, Halsey was loud and profane. Yet in the dark days of 1942 they forged a winning partnership in the Pacific. After Pearl Harbor, when Admiral Nimitz took over command of the Pacific Fleet, he quickly realized that the one carrier admiral he could trust with any mission was Bill Halsey
Edwin Hoyt, Closing the Circle
So, of course, Nimitz was on Team Halsey in 1942 and 1943.
I am more impressed with his actions later in the war and in the post-war period. Victory not only has a hundred fathers, it also brings forth a thousand quibblers and scribblers and ankle-biters. Halsey was (and is) a frequent target for that crowd.
We lack eyewitness records of what happened next, but we know that Halsey barged into the CinCPac conference that day or the next and cleared the air by sounding off loudly, and no doubt profanely, against the defeatism he found. He then and there permanently endeared himself to his commander in chief by backing him and the raiding plan to the hilt. Because he was a vice admiral and Commander, Aircraft, Battle Force, and was liked and respected by all, his words carried decisive weight. Long afterward, when Halsey came under criticism, Nimitz recalled this difficult period and refused to participate in the general censure. "Bill Halsey came to my support and offered to lead the attack", he said. "I'll not be a party to any enterprise than can hurt the reputation of a man like that
E. B Potter, Nimitz
Supporting the man who supported you even when you no longer need his support. That’s loyalty. And without reciprocal loyalty, real leadership is impossible.