there are couple so called 'dog run' here in singapore where you can let your dog has his right to run free. unfortunately have no detail for you
but apart from that, you can 'sneakingly' let your dog runs free at mac richie reservoir (get there early in the morn when nobody with faint heart is around). another place is pulau ubin (if he is very obedient to your call, since if not, he might get excited and catch wild lizards and get biten by snake). and maybe Sungei Buloh reservoir? Ive never been there tho, so im not really sure either
hope your dog can run freely soon!