Ku qor sii wadida cutubkan - Bishii Sebtember 2013, Gedevanishvili wuxuu kaalinta lixaad ka galay Nebelhorn Trophy
, tartankii u dambeeyay ee isreebreebka ciyaaraha Olombikada. Natiijada kaalinteeda, Georgia waxay heshay mid ka mid ah lixda boos ee haweenka ee loo heli karo dalalka aan u qalmin 2013 Worlds. Gedevanishvili wuxuu u beddelay tababarayaasha Brian Orser iyo Ghislain Briand ka dib taxanaha Grand Prix. Gedevanishvili wuxuu kaalinta 10-aad ka galay tartanka Yurub iyo kaalinta 19-aad ee Olombikada Jiilaalka ee 2014.