A "three-album record deal" is a contract with a record comany to produce three albums over some period of time (an "album" is a collection of songs, traditionally on a vinyl LP or a CD). "held" means something like "possessed", but the phrasing of "has held a three-album record deal" seems slightly vague to me. I suppose it means that this deal existed at some point in the past, but not necessarily now.
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