Delegation of authority has a wider meaning than "substabelecimento". Delagation of authority does not include the need for the principal to have first received their authority under a power of attorney. In Brazil, the terms "substabelecer" and "substabelecimento" are very commonly used in powers of attorney granted by a client to an attorney for representation of the client in legal matters. Usually, this power of attorney will contain a "substabelecimento" clause saying that the attorney is allowed to delegate the powers granted to him/her to other attorneys in the law firm.
Delegation by the principal to a third party of the authority granted to the principal under a power of attorney.