Honestly speaking, Karma is not exactly a strong pick right now. This guide mainly focuses on a new playstyle on Karma so she don't get restricted to speeding up her teammates and hope they survive teamfights. To achieve this goal, there are some things we need to change up from the typical Karma build:

1. Stats
While AP is important to Karma, as a support you are not going to have enough gold to get AP items that are enough for you to heavily impact the game. Thus, Ability Haste will be our focus instead, and this synergizes well with the build we are going.

2. Team contribution
Unlike most other support champions, Karma does not really have much CC. She only has a slow from her Q and a root from her W which takes some effort to land. The typical Karma will provide utility to the team by speeding up teammates with Shurelya's Battlesong, or with empowered E that gives your entire team a shield and movement speed. However, doing so will mean that Karma will almost do nothing for the rest of the teamfight due to the cooldowns. The twist this build provides is to give Karma more consistent damage by building Liandry's Torment, and going Rylai's Crystal Scepter for the slow to provide some extra utility in teamfights. Also, picking Glacial Augment will mean landing a W provides much more utility in teamfights, and if the enemy engages on your carries, the 15% damage reduction can possibly save them and create room for outplays.

Typical Karma build with Luden's Tempest will try to stack a lot of AP so she can do damage with her Q and shield for a little more damage with her E. However, we all know supports typically aren't very rich. Building Luden's Tempest will almost always mean that you will have 0 impact when behind, and even if you are ahead, the enemy can simply just do more damage with the same build. Similarly, building Shurelya's Battlesong will make Karma into a fully utility champion and does not contribute much to teamfights.

Thus, instead of focusing on AP, we will deal %hp damage with Liandry's Torment, and stack Ability Haste instead to provide more consistent burns, and at the same time, more consistent slows from Rylai's Crystal Scepter. Usually, you will want to complete your Ionian Boots of Lucidity first so that together with your E, you can have more roaming potential and disturb your enemy midlaner more. However, it is usually recommend to have purchased at least two Amplifying Tome before that so you can actually do damage. Early on, the raw damage on your Q with some AP can be really strong, just that it also falls off quickly so try to get more impact early on. (If you do not plan to roam alot, you can change the secondary runes to Transcendence and Gathering Storm instead.)

You can either complete Liandry's Torment or Rylai's Crystal Scepter next depending on what you need more. If you are at a risk of dying alot, you can also get Rylai's Crystal Scepter first before your Liandry's Torment. If not, rush to get your Liandry's Torment power spike. Future's Market will help with the rush. Once these 3 items are complete, you are basically done with the build and can just grab any item you seem fit afterwards.