I know he has a few credits in the 50s as a voice over but I cant find much else about him and consequences of his role for Nazi Germany in WW2.
According to the encyclopedia of German voice over actors, Harry Giese was in West-Berlin after the war, specifically in the American zone, where he underwent the regular denazification process. In the US Zone in Germany that meant filling out a several page questionnaire of the Office of Military Government for Germany (OMGUS), which also did investagtions of the people they questions, mostly in form of checking the NSDAP membership lists and the lists of membership for the SS and other party formations.
Giese had not been a member of the NSDAP. He was however deeply involved in the Nazi film industry and participated as a speaker / voice actor in movies like Leibstandardte Adolf Hitler im Einsatz (Leibstandarte Adolf Hitler in Action) and – notoriously – Der ewige Jude (The eternal Jew), which is known as one of the most heinous Nazi propaganda movies Goebbels and his people produced. Still, since he was not a member of the Nazi party, OMGUS classified Giese as a "fellow traveler" at most and so he was not barred from continuing to work or had to suffer any other sort of consequences. This is the reason why he was able to resume his work as early as 1946 with productions such as Mädchen im Rampenlicht (Ziegfield Girl).
Giese was rejected as voice over for the newly established Wochenschau in West Germany in 1952. He continued to do a lot of work in advertising and with smaller roles in German movies. In 1960 in one of his later roles he did voice over work for the trailer of the explicitly anti-Nazi film To be or not to be by Ernst Lubitsch. This bears a particular terrible note since Lubitsch was one of the people who had been subject of anti-semitic ridicule spoken by Giese in Der ewige Jude.
After 1960 roles dried up and Giese who was born in 1903 was in an appropriate age for retirement as well. The encyclopedia claims that in later years, it was mostly his wife, Gertrud neé Linkowski, who supported the couple financially – she worked as an Oberstudienrat, meaning a government official in school adminsitration. In his later years, he lived very secluded live and dies in 1991 in Berlin.