To see, or move through, a turnstile in your dream symbolizes new opportunities that are opening before you. You may be entering into a new stage in your life, or exploring your inner self more deeply.
To dream that the turnstile is locked or closed and you cannot move through it, signifies lost chances or opportunities that are denied to you.
If you are outside a place trying to get in, the dream reflects some anti-social tendencies you have.
If you are inside trying to get out of somewhere, then it represents lessons you need to learn in order to grow as a person.