The line of fire was the area in which one was vulnerable to being hit by weapons fire.
In 2153, Major J. Hayes believed Malcolm Reed's security team was too valuable to put in the line of fire, preferring to deploy his own instead. (ENT: "The Xindi")
In 2268, Claudius Marcus told his men to halt, as he and they were within each other's line of fire. (TOS: "Bread and Circuses")
In 2372, Tom Paris questioned Tuvok's navigational instructions, "mark four zero", noting that USS Voyager would be within a Cravic ship's line of fire. The Vulcan explained that their fire was opening a rift in the Pralor defense field, which Paris realized their ship could then exploit. (VOY: "Prototype")
In 2373, Kathryn Janeway disputed Chakotay's suggestion that Voyager withdraw and allow Species 8472 and the Borg to fight against each other, as six months to a year later, they might be right back where they started, in Species 8472's line of fire. (VOY: "Scorpion")
In 2375, Ezri Dax assured her brother Norvo Tigan that he was out of their mother Yanas Tigan's metaphorical line of fire (nagging), as the Trill was busy bothering their brother Janel Tigan and Miles O'Brien instead. (DS9: "Prodigal Daughter")