 Nyorai kupfuurira kweiyi ndima - Zaremba akaberekerwa muMoscow mumhuri yevaimbi, uye akadzidza paGnessin State Musical College, achijoinha Bolshoi Opera muna 1984 apedza kudzidza. Pakushanya kwekambani muna 1989 kuLa Scala akaita kutanga kwake kweWestern saVanya mu Hupenyu hweMambo. Panguva ino mubasa rake akaimba zvikuru mabasa echiRussia, akadai saLaura mu The Stone Guest, muchengeti wemba muBoris Godunov, Olga muEugene Onegin, uye Amelfa muThe Golden Cockerel; mamwe mabasa aisanganisira Cherubino naLola muCavalleria rusticana. Muna 1990 Zaremba akabatanidzwa saKonchakovna kuMuchinda Igor paRoyal Opera House, chiitiko chakachengetedzwa pavhidhiyo. Muna 1991 akaimba muNew York neBolshoi iri parwendo; muna 1992 akanga ari Ulrica paVienna State Opera, uye gore rimwe chetero akaimba Carmen nokuda kwaBregenz. Muna 1991 akatora chikamu mukutanga kwenyika kwe The Master naMargarita naNicolas Slonimsky muMoscow. Zaremba kubvira ipapo akatamira kuMadokero, uye akatora mabasa akadai saDalila. Akaimba kakawanda neMetropolis Opera kubvira paakatanga nekambani seAzucena muna 1999. Zaremba akarekodha basa raErda mu Das Rheingold pasi paChristoph von Dohnányi, asi ruzhinji rwekurekodha kwake rwemimhanzi yeRussia. 