It depends on your contract. Arkansas State Real Estate Contract has 3 choices:
A. No termite will be done
B. Seller pays for a 1-year termite contract for the buyer
In most cases in this area, B is chosen and it's up to the Seller to choose a company (if there's not already a termite contract on the house), order the inspection, and pay for it at closing. Sometimes the title company will order, but it will be from a company the seller has chosen.
If the buyer is paying, it's up to the buyer to do so (and C would be chosen and that written in).
A good agent will help the buyer or seller get these items done. Termite "inspections" are FREE in this area (Rogers, AR). The 1-year policy required by most lenders costs an average of $300-500 unless there is termite damage or low clearance under a crawlspace house. Your agent can tell you all of these things and more!
Let me know if this helps.