The phrase "chase skirt" is an informal, colloquial idiom often used to describe a man pursuing women, usually in the context of romantic or sexual interest. It has a somewhat dated and casual tone, and depending on the context, it can carry either humorous or negative connotations.  
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دختر بازی کردن
مترادف: Flirt, womanize, pursue women, chase romance. 
مثال؛
He spent his college years chasing skirt instead of studying. 
John’s friends teased him, saying he’s always chasing skirt at parties.