Does Jaws 1 have a similar extended edition like this one?
Yes. There’s a television version from (November) 1979, that’s about six minutes longer than the original 1975 theatrical release. As this was screened for network television, it’s been edited for language & violence.
Almost all the extra footage has been released (in widescreen) on Laserdisc, DVD and Blu-ray disc.
*Near the beginning of the shark hunt, there’re two quick insert shots of Quint’s fishing tackle box. The two shots are exclusive to this television cut, and haven’t (to my knowledge) been released on home video.
I have been hoping for a long time now, that this television cut will get a home video release one day.