。
Her popularity as a singer is on a sharp upswing.
Literal
She [topic-は] singer [as-として] popularity rapid-rise [in-progress-中] is.
人気急上昇中 reads like a magazine headline — and it is, basically. 急上昇 ('sharp/rapid rise') + 中 ('middle, in the middle of') gives 'currently rising sharply,' a common framing in entertainment news. The 中 suffix attaches to nouns and verbal nouns to mark something currently happening: 工事中 ('under construction'), 会議中 ('in a meeting'), 急上昇中 ('rapidly rising'). である is the formal copula; combined with the journalistic phrasing, the whole line reads exactly like a news byline or industry report.