The Super Saiyan was an iconic transformation of Dragon Ball, inserted during the Freeza arc. From that point on, however, this mode has expanded in various degrees and levels, and Dragon Ball Z ended with Super Saiyan 3. But only Goku and Gotenks managed to reach this level, while the Saiyan prince Vegeta did not.
In Dragon Ball GT Vegeta directly reached the Super Saiyan 4 stadium taking advantage of a device built by Bulma, but as we all know now there is Dragon Ball Super that could rewrite this story. Vegeta Super Saiyan third level is indeed a forbidden dream of fans and this has led to the inclusion of this unpublished character also in some video game of the saga.
But it still makes sense to add Vegeta to that level in Dragon Ball Super? As we have seen, the transformation into God has now taken hold, not to mention the new Ultra Instinct which could replace the Super Saiyan in its entirety. Therefore now the end of the dreams of those fans who wanted to see Vegeta with very long hair seems to have come, as happens to the rival Goku.
With the latest events of the Dragon Ball Super manga designed by Toyotaro, among other things, it seems to be still there less likely to see Vegeta in Super Saiyan 3 version.