This is my Tenet Livia quick attacks/utility build for running with Trinity. This build does not prioritize maximum damage per second, but rather ease-of-use, which is why the [Tenet Livia] is selected in the first place.
[Tenet Livia] can build up its combo quickly using [Guardian] Derision thanks to its blocking passive, then retain that combo count when stowed. This also helps Trinity focus on a defensive/support role when needed.
I prefer [Gladiator Vice] over [Primed Fury] because the 1.41 attack speed just feels right to me. Plus, half the time there's a [Wisp] or something buffing your attack speed to the animation limit anyway. :P
[Carnis Mandible] is technically worse than [Buzz Kill] for sustained DPS, but since this is a quick attacks build I prefer to have the slight bump in initial status chance. The difference between these mods is very minor (especially given we are running [Weeping Wounds]) and up to preference. Typically when we are killing an enemy with this weapon, we have already primed them with another couple status effects and are simply cleaning them up. This build does tend to deliver more Viral than Slash procs on paper, but you can use [Wise Razor]'s Calling Thunder combo to force a slash proc on the first attack, or a very powerful forced slash proc on the heavy attack when appropriate.
My riven is mainly used for critical damage bonus, so replace it with [Gladiator Might] if you don't have a similar riven. The reason I like this particular riven is for its +4.9 combo duration. Strictly speaking, it isn't necessary to use a combo duration mod on the [Tenet Livia] thanks to its passive, but I like having a few extra seconds of leeway since, as I mentioned, this build is also meant to support a slightly more passive play style.