The heat rejected by the engine is collected by the heat sink which is at lower temperature than the source. My question is : Is it possible to use the heat from the heat sink for further expansion of the gas to do more work and incerease efficiency
Yes it is, such secondary work extraction devices are called topping cycles and pull a little more useful work out of the flue gases from a conventional thermodynamic cycle. One popular form of a topping cycle is an absorption cycle refrigerator that runs off the waste heat in the flue gas; these things are commonly used to furnish air conditioning in office buildings near the flue stack. Since they run on waste heat, they are very cheap to operate.
As progressively more work is extracted from the flue gas exhaust, its temperature falls towards ambient and the efficiency of any process intended to extract useful work from it falls towards zero. This makes further work extraction impractical.