How do you get the Season 2017 - Solo/Duo Gold?
It was a ranked reward. Riot's description in the client reads: “Earned by achieving Gold in the 2017 ranked season in Solo/Duo.”
Is the Season 2017 - Solo/Duo Gold still available?
No. The Season 2017 - Solo/Duo Gold was a ranked reward. To earn it, you had to reach Gold in Solo/Duo during Season 7 (2017). Riot does not hand out past ranked rewards again, so you cannot earn this icon anymore.
