Mezue ahịrịokwu na-esonụ: Ọ malitere 2013 site na ijuputa na United States na German ìgwè n'oge
2013 Hopman Cup dị ka onye nnọchi maka mmerụ ahụ John Isner na Tommy Haas. Kokkinakis gbara asọmpi asọmpi nke 2013 Australian Open, na-efunahụ Steve Johnson 15 <unk> 17 na nke atọ. Kokkinakis merụrụ ahụ n'azụ ya n'egwuregwu Australian Open nke ụmụ nwoke nke mere ka ọ ghara ịsọ mpi ruo etiti afọ 2013. Mgbe ahụ ọ laghachiri asọmpi na-egwu asọmpi Futures na Czech Republic, Canada na United States na isi ihe bụ nkeji iri na ise nke ihe omume Canada F5. N'ọnwa Septemba na Ọktọba, Kokkinakis gbara asọmpi abụọ nke Challenger na United States. Nke mbụ bụ 2013 Napa Valley Challenger ebe ọ ruru eru wee ruo agba nke abụọ, na-agbada Bradley Klahn n'agbanyeghị na ọ na-ebute ụzọ site na set. Mgbe ahụ na 2013 Sacramento Challenger ọ tozuru oke wee mee agba nke abụọ. Ọ tụfuru ọzọ n'agbanyeghi na ọ na-ebute ụzọ site na setịpụ megide Nick Kyrgios. N'ihi nke a, ọkwa ya gbagoro n'ọkwa nke 655. N'ọnwa Ọktọba, Kokkinakis na Benjamin Mitchell jikọrọ aka wee merie Melbourne Challenger na-emeri Alex Bolt na Andrew Whittington na njedebe na setịpụrụ. Nke a mere ka ọkwa ya dị elu site na ọkwa 453, nke mere ka ọ dị elu na ọkwa 505. Ọ gakwara agba nke abụọ n'egwuregwu ndị otu. O yiri ka ọ ga-akpata nnukwu ọgbaghara mgbe o merisịrị Matt Ebden setịpụ nke mbụ tupu o tufuo setịpụ abụọ na-esote. O mechiri afọ ya na 2013 Traralgon Challenger ebe o meriri na agba nke abụọ na James Duckworth na setịpụrụ.