"Subject to" means "under the control of." A candy bar might have a prize coupon in it. The coupon says "Scratch off the covering. If you see three dollar signs, you win $1,000! Subject to local law." Some places might have laws in which this would be a kind of gambling, and illegal. The words "subject to local law" is a short way of saying "You win $1,000, unless you live in a place in which this game is illegal, in which case you don't." In your agreement, it means "the agreement shall terminate on 31/12/2009 unless something else in this agreement says something different." You need to read through the whole agreement. You need to see if there is language somewhere else that says "if thus-and-such happens, the agreement shall terminate."

subject to, here has a similar meaning to "depending on". Subject to availability =depends if there is any available. Subject to any provision = depends on the provisions stated in the contract. "subject to any provision to the contrary in this agreement" = depending on whether a provision stated elsewhere in the contract is met, then this contract will end on 31/12/2009. It is a very common phrase in contacts, rent leases etc. Maybe there is a provision that states, if the tenant starts a fire then the contact will end. Maybe there is a provision that states, if the employee is always late then she will be fired. Understand? That was a tough question!

This is tricky, legal language but "subject to" means that it is dependent or conditional on that happening. So, I believe this is saying that as long as there's not a provision stating a different ending date, the ending date will be 31/12/2009.