To avoid wasting the priority you've secured, please stay on the line without hanging up.

Literal

Acquired priority-right [obj-を] waste-do not-[in-order-to-ないために], as-is cut-[without-ずに] wait-please.

A formal phone/queue announcement. 獲得した is the past form of 獲得する ('to acquire') used attributively as a relative clause modifying 優先権. 無駄にする is the fixed collocation 'to waste.' ~ないために marks the negative purpose ('in order not to X'). 切らずに uses the literary/formal ずに ('without doing X'), more formal than ないで — typical of announcements and written instructions. お待ちください is the standard polite imperative using the honorific お-prefix plus ください.