By the tender age of 21, the Scot had collected the League Cup, scored in an epic Scottish Cup Final victory over Celtic and forever etched his name into Ibrox lore by being a member of the team that achieved European glory in Barcelona.
Enough, you might think, to be highly thought of for the rest of the days.
Alfie, however, committed the cardinal sin of crossing the great divide and signed for Celtic after three years in England with Tottenham.
Such is the rivalry in the world of the Old Firm, his decision was seen as treacherous.
Even now there are those who are still unforgiving but time has been a great healer and Conn insists that Rangers are still his first love.
Nevertheless, he signed for Jock Stein in March 1977 and the irony is that he won his only league championship medal with the Parkhead club that year.
He further infuriated the Light Blue Legions by helping Celtic to victory in the ’77 Cup Final, becoming the first man to win medals with both sides of the Old Firm.
It was four years earlier that Alfie had starred for Rangers against Celtic in the Centenary Final , which finished 3-2 in the Light Blues’ favour, and it is a memory he cherishes.
But his greatest moment undoubtedly came when he helped Rangers lift the European Cup Winners Cup with a 3-2 win over Moscow Dynamo.
It was not a great surprise that Conn became a Rangers great as he came from great football stock.
His father, also Alfie, is a legend down Tynecastle way as he was part of the famous strike force of the 1950s which was known as the Terrible Trio.
Conn junior, however, also made a name for himself in England when he was signed by Spurs and he was sensational in his first season.
The club was in desperate trouble at that time but Alfie managed to keep the crowd enthralled with his brilliant skills and flair.
He scored a sensational goal as Tottenham beat Wolves 3-0 at White Hart Lane and was absolutely brilliant throughout the game, leaving the London side just six games to go to stay up.
A 1-0 away win at QPR was followed by a 2-1 home win over Luton. When Spurs went on to lose 3-2 at Burnley, things looked bad.
However, Alfie lifted Spurs to great heights in the next game at home to Chelsea when 50,998 watched the game.
Chelsea had both the Wilkins brothers in their team, with a young Ray Wilkins as captain.
His brother, Graham was sent off and Spurs survived the pressure well to win 2-0 with Alfie again brilliant in his dribbling and shooting and creating chances for the others from the wing.
Now there were just two games to go. A 1-0 reverse at Highbury against Arsenal left Tottenham having to win the last game of the season to stay up.
It was at home to Leeds on Monday April 28, 1975 and Leeds had a European Cup final to play later that week.
Spurs were absolutely brilliant that night and Alfie’s skills inspired them to a 4-2 win and he bagged one of the goals.
During this period, Conn earned his only Scotland caps although they produced mixed memories.
He came on as a sub as Scotland beat Northern Ireland 3-0 and played the whole game as England thumped Willie Ormond’s team 5-1 at Wembley a few days later.
He ended up Motherwell in 1981 under Jock Wallace after a spell in America with Pittsburgh and a season with Hearts.