You should have a termite inspection no matter where you live and if there is evidence of termite damage the home should be treated by an exterminator prior to closing. But where I live and work, it is up to the buyer to have the inspection done. Check with your realtor and lawyer to find out what is customary in your area.
A clear CL-100 is required in most cases by the lender. The contract should stipulate whether it is the buyer or the seller's responsibility to have the termite inspection completed and paid for. Your real estate agent should be able to answer your question and instruct you as how to negotiate this portion of the SC contract.