"From his presence, I feel that I am glimpsing a man of great talent."
大器 = (この文脈では)a person of great talent; a man/woman of great talent; great talent; greatness
片鱗 = (この文脈では)a glimpse; a snapshot
雰囲気 = (この文脈では)presence; aura; air
感じる = feel
「大器の片鱗」= "A glimpse of greatness." ; "A glimpse of great talent."
「彼の雰囲気から、大器の片りんを感じる」= "From his presence, I feel that I am glimpsing a man of great talent."