So... this is a build, well actually a couple of builds, me and my friends tested out on PBE. Trust me Zeri is going to dominate New Meta, Nerfs and Buffs will make us play her on Solo Lanes or even Jungle, surely not support tho... for now... Riot has done a fantastic job thinking this specific marksman and I am truly eager to see where this is going to end.

Passive - Living Battery
Zeri gains Move Speed whenever she receives a shield. When she damages an enemy shield she absorbs its energy, shielding herself.

Q - Burst Fire
Passive: Zeri's basic attack deals magic damage, scales with AP, and is treated as an ability. Moving and casting Burst Fire stores up energy in Zeri's Sparkpack. When fully charged, her next basic attack will slow and deal bonus damage.

Active: Burst Fire shoots a burst of 7 rounds that deal physical damage to the first enemy hit.
Burst Fire scales with AD and is treated like an attack, with the first round applying on-hit effects. Its cooldown matches Zeri’s basic attack timer.

W - Ultrashock Laser
Zeri fires an electric pulse that slows and damages the first enemy hit. If the pulse hits a wall it fires a long range laser from the point of impact.

E - Spark Surge
Zeri dashes a short distance and energizes her next 3 casts of Burst Fire, causing them to pierce through enemies. She will vault over or grind along any terrain she dashes into, depending on the angle. Hitting a champion with an attack or ability reduces Spark Surge’s cooldown.

R - Lightning Crash
Zeri discharges a nova of electricity, damaging nearby enemies, and overcharges herself for a moderate duration. While overcharged, Zeri gains increased damage, Attack Speed, and Move Speed. Attacking enemy champions refreshes the overcharge duration and adds another stack of Move Speed. While overcharged, Burst Fire's damage concentrates into a faster triple shot that chains lightning between enemies.

I am not gonna focus so much on the builds, I already wrote a description about them under each of them.

Zeri counters and how to play against Zeri…

Zeri Counters

We will examine Zeri counters under three different headings. S tier Zeri counters, A tier counters and B tier counters…

S Tier Zeri Counters

The easiest way to stop Zeri is to reach her as quickly as possible.

Yasuo: Yasuo challenges Zeri just as he challenges all other marksmen. He can kill marksmen after a single knock up. A hundred percent critical hit is a nightmare for fragile champions.

Zed: Zed is a typical assassin, he can kill any marksmen.

Malphite: Being both a tank and an engager, Malphite can make mobile marksmen offended by the game.

Leona: Leona has the power to do to Zeri the same thing she can do to Kalista. She can single-handedly kill a marksman if she is using the flash and q ability combo instead of using first her e skill.

A Tier Counters

Seraphine: Area-controlling champions block mobile marksmen. So you can use Seraphine in bot lane.

Malzahar: Malzahar has the potential to kill all champions in the game with one ability. Sure, if he reaches.

Trundle: Trundle is powerful enough to stop mobile marksmen. At least he forces them to use their dash skills.

Nocturne: Nocturne both very powerful and an assassin. No other words are needed.

B Tier Counters

Nasus: Nasus w counter champions that all movement speed and attack speed. However, we recommend playing Nasus as ability power, as Zeri is very mobile.

Rammus: Rammus can be played against all marksmen.

Akali: If you are dealing with very mobile marksmen, it might make sense to pick a more mobile assassin.

How To Play Against Zeri?

The easiest way to play against Zeri is to force her to use her dash and start a fight while her dash is on cooldown. Defeating Zeri in the lane is about manipulating the minion waves. If you menage to push the minions on her, you can win the lane and win the game before Zeri reaches the desired power.

Mobile champions are very hard to avoid. That’s why it is very important that you engage for fight yourself. If you are unable to fight, your team must have a disengage ability (Janna, Gragas, Thresh et.) Otherwise, Zeri will surely catch up with you.

Rakan: You need more about this champ? All his kit is an absolute win with all ADCs
Blitzcrank: Q and R Supermacy
Karma
Lulu
Nami
Kassadin

You see I did not right anything about Karma, Lulu, and Nami because I need to say A LOT:

Karma, Lulu, and Nami will all work well with her… specifically because they all have a very short CD for proccing enchanter items.

Staff of flowing water second item if your lane is strong side is a given since:

Zeri has High AP ratios on all her abilities

Her auto attack (Q) speed is based on AH

Her W and E have a medium to high CD

The three enchanters I specified can all maintain the 4 seconds of water staff since they either have multiple ways to proc it (due to Aery) or they have an ability that is <4 seconds in CD (Karma’s and almost Lulu’s E at one point).

Kassadin: Unlike Maokai, Kassadin's passive stacks with both her AA and Q. This is an absolute win!

https://www.leagueoflegends.com/en-us/event/zeri-abilities-rundown/
https://www.reddit.com/r/karmamains/comments/ryk0kx/thought_on_possible_synergy_with_the_zeri/
https://topwordy.com/zeri-counters/
https://www.youtube.com/watch?v=nYOqqKQ4Wc4
https://www.youtube.com/watch?v=c8D9WEwA0ZQ
https://www.youtube.com/watch?v=42ekiCXy90g
https://www.youtube.com/watch?v=pHBNmdI99ZM