He was a teacher at the Sternsches Konservatorium in Berlin from 1866-1868. He then moved to Copenhagen, where he held a position at the town's conservatory for two years. In 1881 he travelled to Moscow, and in 1882 he moved to Christiania (today Oslo), where he taughed at a piano school for children. In 1883 he stayed in New York. Neupert was regarded as an outstanding pianist and piano pedagogue, often compared to Franz Liszt.
He was now best remembered as the soloist on April 3, 1869 at the world premiere of Edvard Grieg's Piano Concerto in A Minor, with the Royal Danish Orchestra conducted by Holger Simon Paulli, in the Casino Concert Hall in Copenhagen. The piano used for the performance was lent for the occasion by Anton Rubinstein, who attended the concert. Grieg himself was not present due to commitments back home in Norway. Neupert was also the dedicatee of the second edition of the concerto (Rikard Nordraak was the original dedicatee), and was said to have actually composed the cadenza in the first movement.
Among Neupert's compositions, especially the '24 Concert-Etüden' and the '24 Octav-Etüden' are highly regarded.