The Islanders vakasarudza wokutanga zvachose mana nguva, kusanganisira mwaka wavo wokutanga kuitawo chirongwa (1972) pavakasarudza Billy Harris, uyewo 1973 (Denis Potvin), 2000 (Rick DiPietro), uye 2009 (John Tavares). Harris akatamba neChitsuwa kwemwaka misere asati atengeswa kuLos Angeles Kings, nepo Potvin naDiPietro vakapedza basa ravo rese reNHL neChitsuwa. Tavares aive nechikwata kubva muna 2009 paakanyorwa uye akashanda semukuru wechikwata chavo kusvika muna 2018 paakasaina neToronto Maple Leafs panguva yeUnrestricted Free Agency. Parizvino Anders Lee anoshanda semutungamiriri. Vatambi vaviri bedzi, Potvin naBryan Trottier (1974), vakatamba mitambo inopfuura 1000 neIslanders, kunyange zvazvo vamwe vasere vakatamba mitambo inenge 1000 muNHL. Vashanu vakasarudzwa vakapinda muHockey Hall of Fame: Potvin, Clark Gillies (1974), Trottier, Mike Bossy (1977), uye Pat LaFontaine (1983
ChiGerman) Vose, kunze kwaLaFontaine, pamwe chete naBob Nystrom (1972) vane nhamba yavo yunifomu yakasiya basa nechikwata.