From Longman Dictionary of Contemporary Englishmake a play for somethingmake a play for somethingTRY TO DO OR GET somethingto make an attempt to gain something He made a play for the leadership last year. → play
Examples from the Corpus
make a play for something• 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. 