New Avengers #14

The cover for this issue is part of a continuous image running across #12-16.

Secret Warriors #25 revealed that John Garrett was a member, along with Nick Fury and Dum Dum Dugan, of The Great Wheel of the Zodiac led by the the time-travelling Leonardo Da Vinci from Jonathan Hickman's SHIELD series. But this organisation splintered into SHIELD, Hydra and others.
The 1st time we actually met Garrett was as a SHIELD Agent in the Elektra: Assassin limited series, where he got blown up and became a cyborg. He then featured heavily in Daredevil, involving of course Elektra, and then in the Secret Warriors series.
He's always been the type of guy to whom the end justifies the means.

Dum Dum Dugan was 1 of Sgt Fury's Howling Commandos in WWII, and Nick Fury took him along when he became head of SHIELD. But Original Sins #5 revealed that Dugan was killed in action soon after and Fury replaced him with an LMD. Thus the Dugan we've seen in nearly all his modern day apps has really been an LMD.
OS#5 also said that the Dugan LMD thought it was the real person. Whenever the LMD 'died' Fury activated another 1 which was led to believe it had recovered from whatever killed it's predecessor. This succession of LMDs believed their long life was due to Nick's Infinity Formula. In OS#5 'Dum Dum' learned the truth and asked Nick not to reactivate him again.
SHIELD (2015) #9 reactivated him and explained that his AI was centrally-located and just animated the LMD. He became leader of a new Howling Commandos comprised of monsters. Now presumably that AI is running a horde of his spare LMD bodies.

Wonder Man led a squad called the Revengers in the Annuals of the 2010 Avengers and New Avengers series. These New Revengers are:-

Angar the Screamer started off in Daredevil #100 and had a varied career including teaming up with Screaming Mimi in Avengers Spotlight #28. He died on a bank job with Mimi in a flashback tale in Thunderbolts Annual 1997, which led to Mimi joining the Thunderbolts as Songbird. Later in Thunderbolts Fixer reanimated Angar as the sonic being Scream, but he died again in TBolts#59.
Both just before and after Secret Wars Angar has reappeared again with no explanation, accompanying Gorilla Man and Ruby Thursday (amongst varying others) in Amazing Spider-Man (2014) Annual #1 and Power Man & Iron Fist (2016) #2. And now he's in the New Revengers.

Asti the All-Seeing is a minor demon who before this gig was only involved in Dr Strange stories, working for Dormammu in Strange Tales #144 and Defenders #10 and for Umar in DrS(1974)#67 and #73.

We met OMNITRONICUS in #5 and I explained his origin there.

Paibok the Power Skrull was 1st seen in Fantastic Four #358. He had been responsible for replacing Alicia Masters with Skrull Lyja in FF#265, and when the FF found out and came to rescue Alicia in #358 he had been turned into a Super-Skrull with powers like Colossus and Ice-Man amongst others. He made some more FF-related apps and then went cosmic in the Annihilation event.

The original Skar was a cyborg working for the Martians in the alternate timeline War Of The Worlds in Amazing Adventures. There was an unexplained twin in the main Marvel timeline who appeared in the Starblast mini-series and its crossover with Quasar, and then in the Maximum Security mini. But this guy is probably the original because last issue Maker said he got him from an alternate timeline where Martians ruled Earth.

Vermin was turned into a human rat and given control of rats by Baron Zemo and Arnim Zola in Captain America #272. But he later became primarily a Spider-Man villain. In recent years he's been part of Hood's gang (but not in their latest Illuminati incarnation).

This White Tiger is Angela del Toro, niece of the 1st WT Hector Ayala. She inherited his Tiger Amulet and powers in Daredevil (1998) #77-78 and hung around in that series except for having her own mini-series during Civil War I. In DD#113 she was corrupted by the Hand and continued like that through to the Shadowland event.
She was apparently arrested after that, and the Amulet passed to Hector's young sister Ava Ayala who was the new WT in Avengers Academy, Mighty Avengers (2013), Captain America & MAv and now this series.
But Maker rescued Angela from prison, gave her the power back via a Tiger Amulet from another timeline and recruited her into his Revengers. She then took the original Amulet from Ava, gaining twice the power and leaving her young aunt powerless. All this in #7.

That's the last of the New Revengers.

The Zebra Kids, or Children Of The Sun, were created in the Savage Land by 1 of Ex Nihilo's Origin Bombs in Avengers (2012) #4. 2 of them in particular worked with Sunspot later in that series, and came with him when he took over AIM leading into this series.

Max Brashear is a son of Adam Brashear/Blue Marvel. His story was told in MAv(2013). He became science-villain Dr Positron to fund an attempt to rescue his brother Kevin from the Neutral Zone dimension. But he joined forces with his father for a rescue attempt during CA&Mav. And completed his redemption by joining Sunspot's AIM as head of Theoretical Physics. (Kevin is still lost, and Adam has met him again in Exo-Space in Ultimates #4.)

Dr Toni Ho was invented for this series. She is the engineer daughter of Ho Yinsen who helped create Iron Man's armour way back in Tales Of Suspense #39.
The Rescue armour was created for Pepper Potts in Iron Man (2008) #10 during Dark Reign. But Tony Stark took it away from her in the renumbered #527. However a backup Tony Stark AI built her a new version to fight Superior Iron Man in #8-9 of that series. But next issue Toni will say her suit is another 'copy' she designed herself.
Toni Ho in a Rescue armour is an echo of Toni Yinsen/Kid Rescue in the Captain Britain & Mighty Defenders mini-series during Secret Wars.

When Angar died in her arms in TBolts Annual 1997 Screaming Mimi screamed so hard she wrecked her vocal chords and lost her power. When she joined the TBolts Fixer gave her artificial vocal chords and tech to simulate her power as Songbird.

Sunspot's had his cough since at least #4. He's suffering from Terrigen poisoning. Is this why he's not been using his power in this series?

This Warlock is 1 of the alien Technarchs, techno-organic beings, who fled from his father Magus and joined the New Mutants in their #21. He was last seen before Secret Wars in All-New X-Factor.