The ties that Gintoki has to his former life as Shiroyasha live on mainly through his connections with his three former Joui War veteran comrades: Takasugi Shinsuke, Katsura Kotarou, and Sakamoto Tatsuma. The four of them together were members of the old Jouishishi, a faction of samurai rebels who were fighting to expel the foreign Amanto aliens. Though the war began about 20 years prior to Gintama, the Joui 4 were mostly involved in the later part of the resistance. Gintoki, Takasugi and Katsura have all known each other since their youth--as young boys they trained under the tutelage of Yoshida Shouyou (known affectionately as "Shouyou-sensei") and to this day have all been connected to one another and shaped by his teachings. The teachings of Shouyou-sensei have left a strong impression on all of them, and while both Katsura and Takasugi still hold onto the old textbook which their teacher gave them, Gintoki claims to have thrown his away a long time ago. Much of how they came to meet or what their relationship was like at this age is still unknown, but it's certainly no mystery that at one point all of them were very much involved in each other's lives.
However, much has changed since those days. Rather than fighting back to back with one another, they're find that they're caught pointing swords at those who they used to call "friends". With all four of them choosing to live life his own way after the war, it has become difficult for them to see eye to eye. But no matter how stupid or evil Gintoki believes his former comrades to be, he shares an unbreakable bond with each one of them. You know, they're kind of like the people you can't defriend on Facebook without everyone else making a fuss about it.
ONE-EYED EXTREMIST FACTION LEADER, TAKASUGI SHINSUKE.
There's something to be said about a guy whose first appearance in a manga is surprising the main character from behind and poking him with a sword, but I digress. After the Joui War, Takasugi Shinsuke continued on to lead a radical Joui faction called the Kiheitai, and has assassinated many Bakufu officials, all while planning to stage a large scale coup d'état. As someone who only shows up maybe twice every 100 episodes, he can't make #1 on a character popularity poll, but he's most definitely #1 on the list of Edo's Most Wanted. Takasugi despises change, and his idea of saving the post-Joui world that's gone to hell is completely destroying it. With a bad attitude like that, it's no surprise that Takasugi is probably the former comrade most disgusted with Gintoki's acceptance of the post-war world. The two share dramatically different opinions on society: Gintoki welcomes his new life and works to help the people of Edo while Takasugi has a deep-seated hatred for the world and believes the country should burn to the ground for taking the life of their beloved Shouyou-sensei.
It's difficult to pinpoint exactly what Gintoki and Takasugi's relationship was like prior to their fall out after the war, but the short Shiroyasha Koutan spoof trailer shows the two of them joking around, defending one another in battle and even fighting side by side. With the admiration the two shared for Shouyou-sensei it wouldn't be surprising to assume that at one point these two were very close friends who fought together to uphold the ideals of their teacher. After all, the connection that they used to have is the only real basis we have for the current animosity between them now. Gintoki and Takasugi both seem to despise one another for the ways that they've changed and the new paths they have taken. However, no matter how much Gintoki or Katsura may (or may not) lament how their former comrade's new direction, Takasugi believes that nothing has changed since the past--it's simply their paths that have diverged.
It's true that in the beginning we started out in the same place. But ever since then we've all been walking a different path. Everyone did what they wanted. We all watched each other as we slowly drifted apart. I haven't changed at all.
--TAKASUGI SHINSUKE, SHINYAKU BENIZAKURA-HEN
Takasugi is one of the main antagonists of the series despite the fact that he never really does anything and has yet to really display his skills as a swordsman. However, after meeting with Takasugi during the Benizakura arc, both Gintoki and Katsura swear to him the next time the three of them meet, they'll be the ones to cut him down, regardless of the fact that he was once someone they considered a comrade.
ZURA JA NAI, KATSURA DA! IT'S GOOD WHEN THE TERRORISTS ARE ON YOUR SIDE.
Katsura Kotarou (or "Zura" as he is lovingly called despite hating the nickname) takes on a more comedic role in Gintama: not unlike Takasugi, Zura continues to fight for the good of the samurai as a terrorist under the current Jouishishi. However, Zura has no desire for the people of Edo to suffer for what has happened within the corrupt Bakufu. This doesn't make him any less of a wanted man, but he still pops in every now and then much to Gintoki's dismay. The two seem to share a sort of love-hate relationship with one another: despite his very serious demeanor and dedication to his work, Zura is probably 90% idiot and for the most part Gintoki can barely stand the sight of him. Zura also finds himself at odds with Gintoki, whom he initially approached in the series to re-join the Jouishishi and put to use the skills that once gave him the nickname "Shiroyasha". Much to Zura's dismay, Gintoki has long since gone soft and no longer seems to have the ambition or strength which the former "Shiroyasha" displayed on the battlefield. He even advises his beloved sidekick Elizabeth to avoid becoming like Gintoki.
When you follow the way of the warrior, should you eat something sweet like strawberry milk or a parfait your body will stop working and your heart will go soft.
--KATSURA KOTAROU, SHINYAKU BENIZAKURA-HEN
However, the two share a certain kind of respect for one another that Gintoki can no longer find in Takasugi. Both of them strongly believe that something in Takasugi has changed since then, and swear to one another that if either of them change the way that he did, they'll be sure to take the other down. Though Gintoki may really see Zura as nothing more than an idiot and a nuisance, Zura still believes that while Gintoki may appear to be a lazy slob his soul is still burning brightly. He admits to Takasugi that one of the reasons he can continue to live and fight in this world is because Gintoki, who hates this world this most and carries the biggest burden of them all, manages to live on and bear it with a smile. Of Gintoki's former pals, Zura is probably the one who has been inspired most by the way the curly-haired samurai lives life today--even if the majority of the time he only seems to drop by and cause the Yorozuya trouble.
A HA HA HA! HAHAHHAHAHA! AHAHAHAHAHAHAHAHAHA!
Another name to the list of Gintoki's idiotic friends is Sakamoto Tatsuma, whose screen time probably totals even less than Justaways or mayonnaise and consists mostly of his bad habit of nervous laughter. As someone who claims he was never fond of war or fighting, Sakamoto leads the Kaientai, a commercial flying ship that travels the galaxy for commerce and trade opportunities. He believes that everyone has taken their own path towards changing the world and admires Gintoki's ability to assemble people together. When they were younger, Sakamoto had apparently asked Gintoki to join him in space travel, but Gintoki claimed that he loved the Earth too much and didn't think it suited him. However, he did encourage Sakamoto to live life the way he wanted to and urged him to move forward with his plans without him.
Because you were there, I could go into space. Because you stayed here on this Earth, I could run without looking backwards. Gintoki... even if I fall into the Earth, you'll catch me again and I'll fly as many times as I want into space.
--SAKAMOTO TATSUMA, CHAPTER 27
Because of this, Sakamoto seems to hold a fond respect for Gintoki and the way he's choosing to take on the world after their experiences in the war, even if he doesn't understand his way of thinking and can't seem to remember Kintoki's Gintoki's name. Sakamoto is probably the most laid back and ultra-positive of the Joui 4, so he seems to be content with whatever path his friends have chosen so long as they're doing what they wish. Whether or not he'll ever fight again alongside his comrades is questionable--Sakamoto accepted the fate of the country and decided it was time to start advancing with the new era when the rebellion was proving to be a losing battle, and he also no longer wanted to see his comrades die for a useless cause. It's likely that he'll keep floating around in space and continue never appearing in any Gintama episodes again, unless it's to poke fun at his lack of screen time. Ahahaha, ahahahaha ahahaha!