[3.11] Darkning Pact-Necromancer

Dark Pact is a spell that can be cast on yourself or your skeletons.
When cast on skeletons, it can chain 2 times, effectively hit targets 3times, and it can be further increased by using (Awakened) Chain Support.

Besides high base chaos damage which can be further scaled by increasing your minion life, it has a high damage effectiveness(100%) and low cast time(0.5second). If you have 1 added damage to spells, it will yield 6 additional DPS(100% damage effectiveness, hit 3 times due to chain, and cast twice per second). Due to this reason, I choose to scale it by adding extra damages.

Archmage is a support Gem that increase the mana cost of the supported spell significantly, and add tons of lightning damage to it based on the mana cost. I use it to support Dark Pact, to provide huge amount of lightning damage to it.

As a rough estimation, finally 2/3 of our damage is lightning, and 1/3 is chaos.

This glove introduced in 3.11 solves the problem of scaling both lightning damage and chaos damage.
It allows your hits have a chance cause withered, which is a debuff that can be stacked up to 15 times, and increase chaos damage taken by 6% per stack, and this glove also lets Withered debuffs increase elemental damage taken by 4% per stack.
Since Dark Pact hit many times per second, it is easy to reach high number of withered, which significantly increase the damage output.

Dark Pact - Archmage - (Awakened) Chain - (Awakened) Spell Echo - Arcane Surge - (Awakened) Controlled Destruction or Intensity or Concentrated Effects or Hypothermia or something else.

I choose to use Arcane Surge in the main link, to ensure 100% uptime.
You may link it with Arcane Cloak and use another support Gem here.
For the last Support Gem, Intensity or Concentrated deals more damage but yields smaller AOE. If you have a Green socket you can use Hypothermia, since we can chill enemies due to Corpse Pact. You may also consider use Energy Leech to leech some ES.

Vaal Summon Skeletons - Minion Life - Feeding Frenzy
Since we do not need quality on Summon Skeletons, you can buy a LV21 Vaal Summon Skeletons cheaply.
Minion Life increase the life of Skeletons and hence our damage output.
Feeding Frenzy makes Skeletons Aggressively and dash to enemies, which significantly help our clearing.

Assassin's Mark, Desecrate, Firestorm
Socketed into a Shaper Wand with suffix "socketed Gems are supported by Spell Cascade" crafted suffix "Trigger a socketed spell when you use a skill".
Assassin's Mark curse enemies to improve DPS,
Desecrate create corpses.
Firestorm hits enemies several times to stack withered debuff.
If you don't have a Shaper wand with "Spell Cascade", you can use Spell Cascade instead of firestorm.
You can also use a ring with "Curse enemies with Assassin's mark on hit", then you no longer need Assassin's Mark here.

Wave of Conviction-Physical to Lightning, Bone Offering
Sockted into another wand with crafted suffix "Trigger a socketed spell when you use a skill".
Wave of Conviction reduces enemies lightning resistance, which is important since we cannot penetrate lightning resistance now.
We use Physical to Lightning to ensure that Wave of Conviction always reduce lightning resistance.
Bone Offering consumes corpses to trigger Essence Glutton, and provide some survivability.

Flame Dash - Second Wind:
Mobility skills

Arcane Cloak:
Guard skill to improve survivability and damage.

Clarity:
Regenerate some manas, and increase mana recovery when you got "Watcher's Eye".