Wright was the holder of the New Zealand 1000 meters record with a time of 2.38.54[1] set in the Berlin Olympic Stadium on 17 August 1979 until Angie Petty ran 2.37.28 in Tokyo in 2015. Although not recognised as a record at the time Alison's time was eventually ratified over 25 years later. In late 2011, Wright's time of 4:16.7 from January 1981 was also ratified as the official New Zealand women's indoor 1500 meter record though it remained the record for only a few months until it was beaten early in 2012 by Lucy van Dalen. Wright was also the 1500 meters national champion of New Zealand, Scotland and the United Kingdom (indoors).
Wright represented Oceania in the 1979 World Cup Finals in Montreal, Canada. She represented Scotland in the World Cross Country Championships in Madrid in 1981 and the United Kingdom in dual meets in 1981 and 1982. She achieved the 800 meter qualifying standard for the Moscow Olympic Games. Her selection was affected by the international boycott of those Games.
