In November 2020, Conway was named in the New Zealand A cricket team for practice matches against the touring West Indies team. Later the same month, he was named in New Zealand's Twenty20 International (T20I) squad for the series against the West Indies. He made his T20I debut for New Zealand on 27 November 2020, against the West Indies. In December 2020, Conway was added to New Zealand's Test squad, covering for BJ Watling who suffered a hamstring injury.
