Two weeks later on 14 September 2013, Aissati made his Terek Grozny debut in away match, where he made his first start in attacking midfield, in a 2–0 loss against Zenit Saint Petersburg. A week later, on 25 September 2013, Aissati provided assist for Maurício, in a 3–1 loss against Kuban Krasnodar. Having spent the majority of the season on the substitute bench in his first season, Aissati made fifteen appearances in all competitions. He struggled in Grozny for the first six months before finally settling in the country. Aissati also settled in the country by learning a new language during his time there.
