Olimpija was rapidly becoming one of the best football clubs in Latvia then with footballers like Rūdolfs Kronlaks, Ludvigs Dudaņecs, Kārlis Tīls and other future national team players in their top form.
In 1925, Žins scored two goals as Olimpija devastated Cēsu SB 7–0 in the final match for the title of best provincial football club in Latvia.
Playing with Olimpija, Žins won the Latvian Higher League five times and became a three-time winner of the Riga Football Cup (the predecessor to the Latvian Cup).
After winning his fifth title with Olimpija in 1936[1] Žins retired from top-level football together with team veteran Rūdolfs Kronlaks.
In 1927, Žins played for the first time for the Latvia national football team and in his very first match for it his scored three goals becoming the first Latvian footballer to have scored a hattrick in an international match.