The temporal arms race was an arms race involving time travel technology.
Around the 2230s, Section 31, operating on behalf of the United Federation of Planets, discovered that the Klingons were researching time travel, and concluded that they were now in a temporal arms race. To gain a strategic advantage, they developed Project Daedalus, which included the red angel suit.
However, Klingon spies apparently destroyed the suit, after which Section 31 thought they had abandoned the project permanently. (DIS: "The Red Angel")