In terms of time, what is the longest winning streak in sports history?

Antoni Bou of Spain in FIM Trial World Championships (Motorcycling).

The longest (in terms of time) recorded winning streak in any professional sports is Spain's Antoni Bou, having won 34 consecutive FIM Trial World Championship (17 outdoor and 17 indoor) between 2007 and 2023 (as of January 2024, he is still active in the sport).

https://en.wikipedia.org/wiki/Winning_streak

https://wiki2.org/en/Antoni_Bou

If you are happy to include a club, not just an individual, then the New York Yacht Club first won the sailing trophy now known as the America's Cup (named after the yacht that first brought it into their hands) in 1851, and successfully defended it every few years until 1980, a winning streak of 129 years. Since then, the cup has changed hands a number of times.

https://en.wikipedia.org/wiki/America%27s_Cup#Challengers_and_defenders

And the winner of the FIM Trial World Championship 2024 was... Antoni Bou. He extended his streak to 35 wins.

https://www.youtube.com/watch?v=7VOUvDM8iJk