• 嘱託しょくたく — contract/commissioned work; specially appointed staff
• 委嘱いしょく — to entrust; to commission
• 付嘱ふしょく — to charge/entrust with (a duty)
• 嘱望しょくぼう — high expectation; being looked to with hope
• 嘱たのむ — to entrust; to request (literary)

With 口 (speech) on the left, 嘱 is a matter of words spoken: to entrust, assign, or charge someone with a task — often formally.