Destination language seems to be used mostly in the context of immigration (I guess, the language in the new country):
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Language Choice among Immigrants in a Multi-lingual Destination
Abstract: This paper analyzes
the choice of dominant destination
language spoken by immigrants in a multi-lingual destination. The
empirical analysis is performed for Canada. Immigrants tend to
gravitate to the official language that is closer to their mother
tongue, that predominates in their region of residence and that has
the broader labor market or economy. Bilingualism in the two official
languages increases with the level of education in both Quebec and
English Canada.
[link]
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