恐れがある (おそれがある) is a formal expression meaning "there is a risk/danger of ~" or "it is feared that ~". It is used to warn about a negative possibility – something undesirable that could happen. This grammar point is very common in news reports, weather forecasts, official announcements, and written warnings.
The expression attaches to verbs, nouns, or adjectives:
恐れがある is used exclusively for negative or undesirable outcomes. You would not use it for positive possibilities. For neutral possibilities, expressions like かのう可能せい性がある are more appropriate.
Compare:
This is a formal, written expression. In casual conversation, speakers would typically use かもしれない (might) instead. You will encounter 恐れがある most often in: