From Longman Dictionary of Contemporary Englishmake a play for somebodymake a play for somebodyto try to begin a romantic or sexual relationship with someone It’s obvious he was making a play for her. → play
Examples from the Corpus
make a play for somebody• Left alone for a few minutes on Vik's birthday, Karen makes a play for Steve.• Kramer wondered if she was worth making a play for.• Surely only the most decadent of aristocrats would make a play for another woman while his wife was in the same room. 