It is "cards perpetually close to the chest" not "vest" To have "your cards close to the chest" means you are giving away little or no information to other people about your personality, your future plans or future business decisions. The saying originates from playing card games where a player holds his cards close to his chest so other players cannot see what cards he has.

I agree with Steve - the expression is "to play your cards close to your chest" (though I see no problem with using "vest" here). That is, don't give away any information about your plans.