Part II Chemistry has unrestricted admission, but you still need to chose Chemistry within the NST Subjects Allocations Process. You will hear from your DoS about how you go about indicating your choice. See also http://www.cam.ac.uk/about/natscitripos/part_ii/index.html
If you wish to take Part III in 2013/14 you need to make an application to do so. As far as the Department is concerned, submitting a choice of projects using the procedures and timetable described below (follow the link Part III Projects) constitutes a valid application. The deadline for this is 24th May 2013. In addition, you need to satisfy the academic requirements, which are that you obtain at lest a II.1 in Part II Chemistry in 2012/13. Your college may have its own procedures and requirements with which you will need to comply.
If you have submitted your project choices in time, and then go on to achieve the required academic standard in June 2013, you are automatically admitted to Part III in 2013/14 – no further action on your part is needed.
If you do not achieve the required academic standard but still wish to proceed to Part III you can make an appeal using the procedure set out in this document. It is important that make your appeal immediately that you know your Part II result.