。
She is the best pianist after Mr. Long.
Literal
[topic-は] Mr. Long [to-に] rank-after best [genitive-の] pianist [explanatory-です].
次ぐ ('to come next, rank below') is a verb of ordering — used to place something second to a benchmark. The pattern XにつぐY means 'Y, second only to X.' In a relative clause modifying ピアニスト, it gives 'a pianist next to Mr. Long' = 'the second-best after Mr. Long.' The suffix 氏 (し) is a formal Mr./Mrs. used predominantly in writing, journalism, and formal speech — markedly more bookish than ~さん, especially when applied to non-Japanese names. ピアニスト is a loanword.