Unlikely. While lingerie still exists, Gene Roddenberry was adamant that zippers wouldn't even be necessary anymore, replaced by an advanced unseen method of closing clothes (citation needed).
It is highly doubtful that they would use (or Mr. Roddenberry would allow) such primitive shapewear. If there is an equivalent it is probably undetectable and extremely comfortable. But as evidenced by Insurrection, breasts do sag with age. Not that they worry about things like that in that day and age. The latest movie shows bras do indeed exist.