James Bond drove the Aston Martin DB5 in the Tomorrow Never Dies mission around the streets of London. However, the Aston Martin doesn't make another appearance throughout the film.
Production Note- Technically, the Aston Martin DB5 used in Tomorrow Never Dies is not the same one used in the previous two Connery films. The only difference is the licence plate is slightly modified. Instead of BMT214A (the plates in Goldfinger and Thunderball), the Tomorrow Never Dies version reads BMT216A. The reason for this came over legal concerns from the original Aston Martin's owner. Wanting to avoid more legal concerns for United Artists, the producers opted to slightly modify the licence plate.