Alabaster was one of the best leg-break bowlers from New Zealand. He was also the first Kiwi player to be part of the team's first four Test victories. Having not played a single first class game, Alabaster was picked for the tour of Pakistan and India. It was a move keeping in mind the turning tracks in the sub-continent. That selection didn't pay dividends as he picked only 2 wickets in the five games that he played.

However, he picked 2 for 30 and 5 for 99 against a South Zone side at Bangalore. That enabled him to hold his place when West Indies travelled to New Zealand. He took two wickets and helped his side bowl out West Indies for their lowest total at that time - 77. But things went in downward spiral and he was soon left out of the side.

A strong couple of seasons for Otago from 1956 to 1958, where he scalped 36 wickets at 18 which also included a 10-wicket haul against Auckland saw him return to the national side for the 1958 tour of England. He started the tour well with 6 for 37 and 5 for 43 in an innings victory over Leicestershire. And also picked 4 for 46 in the first Test at Edgbaston, but lost his place after the second Test.

Once more Alabaster worked hard and made a comeback for the tour of South Africa. His finest hour came on that tour, in all the first class games, he picked 86 wickets. In the Test matches, he took 22 at 28.04 and helped New Zealand square the series. During the third Test, Alabaster ended with match figures of 8 for 180 - his best in Tests and New Zealand's first win away from home. In the fifth Test, he scalped 4 wicket and became the third player along with John Reid and Noel McGregor to be part of all three New Zealand victories.

Alabaster continued his good work against England in 1962-63 where he picked 5 wickets in two Test. However, his form decreased and he didn't play regularly for Otago as well. His next full season was in 1967-68, another good outing in the domestic circuit meant a call-up to the national side. This time it was versus the touring Indians, he took 12 wickets in 4 Tests. When the Black Caps won the second Test, Alabaster became the only New Zealander to be part of all four of their wins.

Alabaster toured West Indies in 1971-72 at the age of 41. It was his last series in which he managed only one wicket in the two Tests. He hung up his boots after that tour. Life after cricket saw Alabaster become the principal of Kingswell High School in Invercargill. He also became a Rector of Southland Boys High School in Invercargill in 1981.