To give authority to another
authorize, commission, appoint, name, designate, accredit, nominate, select, choose, assign, cast, constitute, license, empower, deputize, depute, swear in, send as a deputy, ordain, invest, place trust in, fix upon, assign power of attorney to, elect, warrant, give one the nod*, give one the green light*, give one the go-ahead*; see also approve 1, commission.
Antonyms dismiss*, repudiate, reject.
To give duties to another
entrust, authorize, charge, assign, give to, hold responsible for, parcel out among, send on a mission, send on an errand, transfer, relegate, shunt, devolve, shove off on*, dump on*, pass the buck*; see also commit 2.
Antonyms maintain*, retain, keep.