The term 'Next in Line' can refer to a variety of different contexts. In this case, the crossword solutions are HEIR and ONDECK. HEIR is a four letter word that refers to someone who is entitled to inherit property or a title from a predecessor. ONDECK is a six letter word that refers to someone who is next in line to take on a responsibility or task. Both words refer to someone who is next in line to take on a role or responsibility.