〜きらいがある
have a (bad) tendency to
Verb dictionary / ない-form + きらいがある · Noun + の + きらいがある
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きらいがある describes an undesirable tendency in a person or group: 彼は物事を大げさに言うきらいがある, "he has a tendency to exaggerate".
The tendency is always negative: exaggerating, giving up too easily, keeping things to yourself, sticking to precedent, not listening. It's a criticism, but a measured and slightly formal one, so it's typical of essays and assessments.
It's written with the kanji 嫌い (dislike), but it means "tendency" here, and it's usually written in kana.
Compare がち (N3), "tend to", which is more everyday and can describe situations (曇りがち). きらいがある is about someone's character.
Don't confuse it with ことがある, "sometimes".
Examples
彼は物事を大げさに言うきらいがある。
He has a tendency to exaggerate.
最近の若者は、すぐにあきらめるきらいがあると言われる。
Young people these days are said to give up too easily.
彼女は一人で問題を抱え込むきらいがある。
She tends to keep her problems to herself.
この会社は前例にこだわるきらいがある。
This company has a tendency to stick to precedent.
彼は人の話を最後まで聞かないきらいがある。
He has a habit of not hearing people out.