The past tense of keep one's cards close to one's chest is kept one's cards close to one's chest.

The third-person singular simple present indicative form of keep one's cards close to one's chest is keeps one's cards close to one's chest.

The present participle of keep one's cards close to one's chest is keeping one's cards close to one's chest.

The past participle of keep one's cards close to one's chest is kept one's cards close to one's chest.