Is it permissible for the head of a charity that provides event supplies to remain in his position, knowing that some of these supplies are used in wedding celebrations that include singing?

If the instruments are used in impermissible singing with your permission or knowledge, then this is not allowed, because it is assisting in sin. However, if they are lent or rented for a permissible purpose and then used in something impermissible, there is no blame upon you. Your remaining at the head of the association is subject to the Sharia (definition)-based interest. If your remaining achieves a greater interest, then stay; otherwise, resign.