Trust is an important concept in many aspects of life, and it is often used in the context of relationships, finances, and other areas. The term 'trust with 'ON'' can refer to two different crossword solutions: RELY and BANK. RELY is defined as having confidence in or placing trust in someone or something. BANK, ON the other hand, is a financial institution that provides services such as deposits, loans, and investments. Both of these terms are related to trust, as they involve placing faith in someone or something.