 Nyorai mberi kweiyi ndima - Mudziviriri wepakati akadzikama uye akaunganidzwa, OLeary akacherechedzwa nokuda kwenzvimbo yake yakanaka uye chimiro chakanaka chokutamba. Akakunda rukudzo rwake rwekutanga rukuru neArsenal paakatamba mukukunda kwavo 3 × 2 kukunda Manchester United mu1979 FA Cup Final. Akatambawo mumakwikwi ekupedzisira e1978 ne1980 Cup, uye 1980 Cup Winners Cup yekupedzisira, iyo yose Arsenal yakarasikirwa. Muna 1982, OLeary akava kaputeni wekirabhu, asi akazvipira kuna Graham Rix mwedzi gumi nemasere gare gare. 