The term 'inaugural' is associated with the BEGINNING of something, and the crossword solutions reflect this. The nine-letter solution, 'INDUCTION, ' refers to the formal process of introducing someone into a new role or position. The ten-letter solution, 'INITIATION, ' is similar in that it is the act of formally admitting someone into a group or organization. The seven-letter solution, 'LEADING, ' implies that the person is taking the lead in the new role or position. The twelve-letter solutions, 'INTRODUCTORY, ' 'INSTALLATION, ' and 'INAUGURATION, ' all refer to the formal ceremony or event that marks the BEGINNING of something. The nine-letter solution, 'BEGINNING, ' is self-explanatory, as it is the start of something. The eight-letter solution, 'FOREMOST, ' implies that the person is the FIRST or most important in the new role or position. The ten-letter solution, 'INITIATORY, ' is similar to 'INITIATION' in that it is the act of formally admitting someone into a group or organization. The five-letter solution, 'FIRST, ' implies that the person is the FIRST in the new role or position. The six-letter solution, 'MAIDEN, ' implies that the person is the FIRST to do something. Finally, the seven-letter solution, 'INITIAL, ' implies that the person is the FIRST in the new role or position.