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Back in the 40's, he was studying to be a concert pianist. He was up for a full
scholarship to the Metropolis Conservatory.
But his teacher recommended somebody else.
Meaning he was going to receive full scholarship
or he received it but didn't enter the conservatory?
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"Up for" most likely means that he had been a possible candidate for a full scholarship (he had applied, his name had been proposed, it was generally thought that he was good enough, etc.). But in the end his teacher didn't recommend him. The implication is that he did not receive the full scholarship, but without knowing what follows it's impossible to be certain. For example, it might continue "... Despite his teacher's lack of support, however, he managed to persuade the directors of the conservatory .... etc."

Whether he received some other type of scholarship, or entered the conservatory and funded his studies in some other way, is not clear just from the piece quoted. In the absence of any further information, I suppose the tendency is to assume that he didn't attend at all.
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today, some would say he had been shortlisted for a scholarship, or perhaps that he had one lined up for him
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