I think the description of Alligators on this site will answer your question.
"An alligator, like a crocodile, in a dream is a symbol of primitive male sexuality, due to its large tail, rigid skin and aggressive behavior during mating season. It is a dangerous animal, which "lurks" in murky water, and can attack without warning. They are common symbols for an aggressive man, which for women may be a suitor or someone who was or may be hurtful in a romantic relationship. Children’s dreams of an alligator or crocodile attack should be taken seriously. They often reflect threats by a male figure in their waking life, including a sexual predator."
If this was my dream, I would ask who the aggressive man in my life is.