The phrase "putting a cork in" typically means to stop something, but there are many antonyms that can convey the opposite meaning. Some examples include: starting, continuing, prolonging, extending, perpetuating, preserving, affirming, or promoting. Alternately, one might encourage, amplify, augment or intensify a situation instead of putting a cork in it. The choice of antonym will depend on the context in which the phrase is being used. Whether dealing with a situation that needs to be stopped or one that needs to be advanced, there are plenty of antonyms to express the desired outcome.