Aubrey started as a teenager in the 1950s with the Sion Mills club. He and another teenager, Brendan Donaghey, formed the youngest ever opening senior partnership (16 and 13 respectively) in North West cricket. They were soon in line for representative honours which duly came for Finlay in the shape of selection for the North West (v NCU), North (v South) and eventually Ireland v West Indies at Ormeau, Belfast in July 1957 at the age of 19. His international debut was a personal triumph for Finlay who scored 29 not out.
Earlier in the 1957 season (June) he scored a great century (113) at Ballygomartin Road, Belfast, when he made his initial appearance for the North West against the Northern Cricket Union. Later in the 1957 season he scored a memorable century (136) for Sion Mills against Strabane in the North West Senior Cup final at Beechgrove, Londonderry.
Finlay played 18 times for his country and was without doubt a stylish and punishing batsman. As his cricket career developed he became a fine all rounder. As a fielder Finlay was also in a very high class and three catches he took in the Combined Services v Ireland fixture at Ormeau in 1962 still reflect brightly in the memory of outstanding feats by Irish cricketers.
In 1973 - nine years after he had last played for Ireland - he hit successive sixes off Dermott Monteith, making 80 in all and putting on 55 for the last wicket with Ossie Colhoun, in a North West Guinness Cup match against Ulster Country.
Finlay also served as an international cricket selector for a spell while in 1971 he joined the Strabane Cricket Club. Although no further honours were won Finlay took part in the 1982 Senior Cup final against St Johnston. He now is an excellent administrator at the Strabane Club.