MTS,
Transferring is regulated by the CIF on a state wide basis, and the individual sections may also have additional requirements. There is plenty of information available on the CIF website
CIF. Scroll down about halfway on the page, and you will see Parent Handbook I - Understanding the Transfer Eligibility Procedure. Reading this will allow you to see whether the student would be eligible to play varsity next year. The actual rules are linked just above the Parent Handbook, and of course are more detailed.
Typically, after the first day of 10th grade, if the transferring student hasn't made a valid change of address, then both the old and new school have to certify that there wasn't undue influence. Otherwise the student can't play at all. Generally, without a valid address change, the student isn't eligible for varsity competition until one year after the transfer. But there are exceptions. Specifically the local section determines how to handle intra-transfers within open enrollment school districts.
If you are contemplating a transfer, you really need to dig deeper than asking on an Internet message board. Eligibility depends on the details of an individual situation.