expression
Describes a face or complexion lacking color, often from fear, shock, or illness. Used attributively before nouns.
彼は血の気のない顔で立っていた。
He stood there with a pale face.
血の気のない唇が震えていた。
Her bloodless lips were trembling.
青白い is a general i-adjective for 'pale' or 'bluish-white', while 血の気のない specifically emphasizes the absence of healthy color from blood, often implying a sickly or frightened look.
Compound of 血の気 (ちのけ, 'sign of blood; color of blood') + の (possessive particle) + ない ('not exist'). Literally 'without blood-color'.