Yes, it was only a rental. No, it didn't have any gadgets to speak of. But James Bond used it to negotiate the treacherous switchbacks in the hills of Jamaica, and to outrace and outmaneuver the "Three Blind Mice" (conveniently following in a hearse) on the way to Miss Taro's villa in Dr. No.

What do we know about the Alpine? Well, this one was a "Series II" Alpine, and they were produced in five "Series" from 1959 to 1968. This is probably a Series II produced from 1960 to 1963. This particular car was "borrowed" from a resident as the only "decent" sports car on the Island (Wikipedia).

Yes, that is Sean Connery skidding through a turn behind the wheel in the picture.

Given that no one has come forth with the whereabouts of this vehicle, it is probably safe to presume that it has been destroyed or has been junked somewhere on the island of Jamaica.