A pledge

assurance, agreement, pact, oath, engagement, covenant, consent, avowal, warrant, asseveration, affirmation, swearing, plight, word, troth, vow, profession, guarantee, insurance, obligation, stipulation, commitment, betrothal, affiance, espousal, plighted faith, marriage contract, giving one's word, gentleman's agreement, attestation, word of honor, parole, warranty, foretaste.

Hope

outlook, sign, good omen, good appearance; see encouragement 2, hope 2.

To give one's word

plight, engage, declare, agree, vow, swear, espouse, consent, asseverate, affirm, profess, undertake, pledge, covenant, contract, bargain, affiance, betroth, assure, guarantee, warrant, give assurance, give warranty, insure, cross one's heart, keep a promise, live up to, plight one's faith, plight one's troth, bind oneself, commit oneself, obligate oneself, make oneself answerable, secure, give security, underwrite, subscribe, lead one to expect, answer for, pledge one's honor, cross one's heart and hope to die*.

Antonyms deceive*, deny*, break faith.

To appear promising

ensure, insure, assure; see encourage 2.