Time Machine back up failure

My iMac 10.6.8 running Snow Leopard recently needed a new hard drive. A local dealer that I have used before replaced the old 320GB hard drive with a 1TB one. I gave the repairer my external drive which had my last Time Machine back up from April 2015 on it in the hope that they could retrieve the current data. They couldn't because the old hard drive was kaput. They replaced the hard drive and installed the April back up which was fine except I'd lost some photos and other stuff I'd inputted since April. I managed to re install some of the lost data and decided to back up. The external drive that I use is a Seagate 500GB. The amount of data to back up on the iMac is just under 250GB. Time Machine starts off fine but then stops and fails because it says the Seagate only has 72.43GB free space and I should try a different drive. As I understand it, once full, Time Machine deletes old data to make way for latest back up, which has happened in the past. I considered erasing the Seagate and trying again but am concerned that once I do that I have no back up if it still doesn't work. Is it likely that I need a bigger external drive now that I have a 1TB hard drive? This doesn't seem likely as I only have 250GB of data to back up. Could it be that the external doesn't recognize the new hard drive? Any ideas?