Nyorai kupfuurira kweiyi ndima - Pashure pokunatsiridza unyanzvi hwake muIrish Formula Ford Championship, Daly akanga ane kutyaira kwake kwokutanga muEuropean Formula Two Championship muna 1977. Muna 1978 na1979, akakwikwidza muFormula Two neFormula One, achipedza ari wechitatu mumakwikwi eFormula Two mumwaka miviri. Kubva 1980 kusvika 1982, akaisa pfungwa dzake paFormula One, gore rake rakanaka raiva 1980, paakawana nzvimbo yechina kaviri uye akapedza 11th muDrivers' Championship. Nguva dzake mbiri dzisingakanganwiki zvikuru muF1 dzose dziri mbiri dzakauya muMonaco Grand Prix. Muna 1980 akadonha zvinoshamisa pakona yokutanga pashure pokudonhedza dzimwe motokari nhatu. Muna 1982
akangoerekana azviwana ari mukukwikwidzana nokuda kwokukunda apo motokari ina dzaiva mberi kwake dzakapinda muzvinetso naasingasviki marunda maviri kuti apedze, asi akaguma ari parutivi amene apo bhokisi rake rinoshandura motokari rakabatwa maminiti gare gare.