Tom never actually gets to give the car to George Wilson. On his final trip into New York city with Nick and Jordan, Tom does promise that he would sent someone over with the car but this never actually happens because George dies before it can take place. At this point in the novel, Tom has realized that this relationship with Myrtle is going to have to end if he wants to take Daisy away from Gatsby. The original reason that he promises to eventually sell the car to George is to have an excuse to stop at his gas station to see Myrtle but now he realizes that George and Myrtle are going to be moving (as George tells him) and knows that the relatioship will end anyway.
There are essentially two reasons Tom decides to acquiesce to George Wilson's request at this point. Firstly, he just discovered that his wife and Jay Gatsby are involved in an affair.
"She had told him that she loved him, and Tom Buchanan saw. He was astounded. His mouth opened a little and he looked at Gatsby and then back at Daisy as if he had just recognized her as some one he knew a long time ago."
This incident occurs in the Buchanan's dining room, after lunch. Tom has just been contacted by a determined George Wilson who wants to buy the car Tom had promised to sell to him. Tom was been upset by his demand, stating that:
"Very well, then, I won't sell you the car at all. . . . I'm under no obligations to you at all. . . . And as for your bothering me about it at lunch time I won't stand that at all!"
Because of what Tom had just seen, he realized that he had much to do to restore his relationship with Daisy, for it was under threat. He had to consider ending his relationship with Myrtle. He had left George hanging and unsure because it provided him with an excuse to visit the garage and make arrangements to meet with Myrtle but in this context, the car issue has now lost its importance.
Furthermore, George emphatically informed Tom later that:
"I've been here too long. I want to get away. My wife and I want to go west."
"She's been talking about it for ten years."
"And now she's going whether she wants to or not. I'm going to get her away."
The realization that he would probably never see Myrtle again made Tom's mind up for him and he finally relented, telling George that:
"I'll let you have that car, I'll send it over tomorrow afternoon."
Tom knows that his relationship with Myrtle is going to end so because of that he dicides to give Goerge Wilson the car that he has been promising for so long.