First of all I love this question and it's a bit of a shame to see it so heavily downvoted. Militaries don't exist in a vacuum. They reflect the societies which raise them and which they serve, and especially for societies like Nazi Germany which were so heavily defined by their wars and their relationships with their militaries, there are a lot of broader insights to be had from questions like this. As two of my favorite military historians recently wrote:
"Examining the origins of wars informs us about human behavior: the way that we create notions of identity, nationality, and territoriality, and the way that we elevate fear and aggression over reason... Combat sheds light on the civil-military relationship within states, and the way that societies are able (or unable) to leverage technology by setting up organizations and processes to take advantage of it. What happens on the battlefield also influences, and sometimes crafts, key social and political narratives."
The quickest answer is that no, the Nazis did not recruit an entirely new military. As an institution, much of the military was continuous with the army of Imperial Germany and then the Weimar Republic. Many of the highly-decorated officers of the Nazi Heer were old Imperial officers. For instance, Field Marshal Friedrich Paulus (the commander of the ill-fated 6th Army at Stalingrad) began his military service just before World War 1 and then served in the Reichswehr of the Weimar Republic before the Nazi takeover. Field Marshal Erich von Manstein was from a very old Prussian noble family; one of his distant great-grandfathers had been a general under Frederick the Great in the 1750s, for example. He too had served in the First World War and then in the Weimar Republic's Reichswehr. Erwin Rommel, the famed Desert Fox, was also a junior officer in the Reichswehr before his meteoric rise to operational command.
These three famous generals don't tell us the entire story, though. There was, as your question suggests, a power struggle between the "Old Guard" of the Imperial Deutsches Heer and the Weimar Reichswehr, and the new blood of the Nazi movement. The Old Guard formed much of the Troop Office (the post-Versailles replacement for the banned General Staff, the group of high-level commanders and theoreticians who had historically run the German military) when Hitler came to power, and initially backed him enthusiastically despite their lack of Nazi convictions. For instance, Ludwig Beck (Chief of the Troop Office from 1933-1935 and then of the General Staff until 1938) was locked in a bitter struggle with more Nazi-aligned generals like Heinz Guderian over Germany's future military doctrine and strategy. This struggle lasted until Hitler intervened on the side of Guderian and the rest of the younger, often National Socialist officers in 1937.
But! The story of Ludwig Beck has still more to tell us about the cultures and attitudes of the German military at the dawn of the Third Reich. You see, while Beck was never a member of the Nazi party, he was very much on board with a lot of the goals of Nazism. Breaking out of the Treaty of Versailles? Check. Annexing Czechoslovakia? Check. ^((czech?)) Upon Hitler's rise to Chancellor in 1933, Beck is said to have written in his diary "I have wished for years for the political revolution, and now my wishes have come true. It is the first ray of hope since 1918." His rift with Hitler came not as a matter of ideology, but of professional disagreement; Beck and other General Staff officers were quite concerned that Hitler would start a war in 1937 or 1938, before they felt that the Wehrmacht would be fully rearmed.
These attitudes were seemingly quite common among the General Staff, despite their postwar claims of apolitical professionalism. Manstein, Paulus, and Halder were all perfectly complicit in mass killings and other war crimes on the Soviet Front, as were virtually all of their colleagues. For brevity's sake I will refer to u/commiespaceinvader's post on the "clean Wehrmacht" as he says it more eloquently than I can. Suffice to say, even though a large number of Wehrmacht officers were not Nazi party members per se, they still accepted and tacitly supported the tenets of Nazism. This mentality was embodied in behavior like the Commissar Order, cooperation with Einsatzgruppen mass-killing squads, and so on.
An army does not consist just of generals and senior commanders, though - it is a mass of millions of enlisted men, non-commissioned officers, and junior officers. This is the part of the Wehrmacht that was largely new recruits. The Treaty of Versailles had limited the Reichswehr to 100,000 men; the Wehrmacht's 1936 plans already called for a wartime force of 3.6 million men, and about 13.6 million Germans ultimately served in the Nazi military throughout the war. This force, much like its commanders, was a mix of dedicated National Socialists, fellow travelers, willing participants, and indoctrinated youths. However, in some ways the enlisted men & the junior officers reflected the total societal reshaping of Nazism moreso than did the senior commanders.
For starters, a large number of the enlisted men had not really known a Germany besides Nazi Germany. An 18 year old recruit called up in 1942 to replace losses at the front would have been nine years old when Hitler took power in 1933 - hardly old enough for any prior political consciousness. Indeed, the Nazi system was quite aggressive in molding the youth via the Hitler Youth and the various propaganda films. As Omer Bartov sums it up in Hitler's Army: Soldiers, Nazis, and War in the Third Reich:
"It was precisely the young combat soldiers of the Wehrmacht who were most likely to have come under the influence of Nazi indoctrination before their conscription. Children aged between six and eleven in 1933 spent long, years in the HJ [Hitler Youth], yet had a good chance of finding themselves at the front during the war." (110)
These young enlisted men (and this is not intended to exonerate them for their many crimes) were very much products of the Nazi social system. One Gustav Koppke, who joined the SS Hitler Youth Division in 1944 at the age of 16, recalled that "I was raised then, in the National Socialist time and had seen the world just as they had shown it to us." These recruits were very different from the men who might have formed the Reichswehr and then the Wehrmacht of 1938-1941. This is especially true when you consider the deep attrition of the first wave of Wehrmacht volunteers in 1941 & 1942 as the Red Army bled the Ostheer in its defense against Barbarossa. For instance, from June 1941 to January 1942, the 12^(th) Infantry Division took 80% of its paper strength as casualties. The portion of these casualties that were killed or too severely injured to quickly return to the front (about 40%) were made up with reserves. Many of these reserves, even in 1942, were fresh 18 year olds. So, in this sense, the Nazis did recruit a new army.
This was probably a longer answer than you expected, but, as with most history questions, there's more than meets the eye, and the answer depends on what exactly you mean by the question. I haven't even touched the SS here, or the Luftwaffe which was a more directly Nazi-controlled branch in some ways. Still, I hope this answer fills in some blank spaces for you and perhaps makes you ask some new questions about institutions and culture in Nazism.