His first-class debut was followed less than two years later by a call-up to New Zealand's T20I squad for the 2012-2013 tour of South Africa. On that trip he played his first T20I at Durban and his first ODI at Paarl. His form for the Otago Volts at the 2013 Champions League, where he helped them win several matches early in the competition, added to his growing reputation.
Neesham earned a Test cap in February 2014, playing against India in the second Test at Wellington. He marked the occasion with a maiden hundred, making 137, which the source describes as the highest debut score by a Test batsman at number 8. That same year Delhi signed him at the Indian T20 League auction, and the Kolkata Knight Riders bought him the next season.
He was not picked in New Zealand's 15-man squad for the 2015 World Cup, a selection call that experts criticised. Neesham took the setback in good humour and kept entertaining followers with his wit on Twitter. A tour of India in late 2016 did not go especially well for him, though he kept a place in the white-ball squad afterwards. He had a decent 2019 World Cup, but uneven returns with the bat have meant he has moved in and out of the national team.
Neesham is regarded as an excellent fielder and a bowler who can keep things tight through the middle overs. He is best known for clearing the boundary with apparent ease, and his ODI strike rate is close to 100, yet he has still to score a white-ball century for New Zealand.