The Taihei Association is the Dojima Family subsidiary operated by Lieutenant Hiroki Awano. According to him, the Taihei handle the "public relations" side of the Dojima Family's business; which is to say, the extortion side of the business.
The Taihei Association also operates a few nightclubs in Kamurocho (most notably Club Deborah in Theater Square) and runs real estate scams, paying people to squat in vacated properties and then extorting the owners to get the squatters to leave.
After Kiryu starts working for the Tachibana Real Estate Agency, he unwittingly foils one of the squatting scams being run by Awano's right-hand man, Okabe. In retaliation, Awano and Okabe beat Kiryu's co-worker, Jun Oda, and then attack Kiryu and his oath brother, Akira Nishikiyama, at Serena. After Kiryu beats Okabe in a fight, Awano gives him until morning of the next day to give up Tetsu Tachibana's location to him, as Tachibana was a bigger target for the Dojima Family.
When the deadline passed and Kiryu hadn't complied, Awano sent his men to scour Kamurocho in search of Kiryu to bring him to him. Ultimately, Kiryu wound up at Awano's club as intended, where Awano renewed his offer to Kiryu, this time also offering a position within the Taihei Association where he could rise up the ranks of the Dojima Family alongside him. Despite Awano's promises of fun and profit, Kiryu rejected his offer; refusing to turn his back on his foster father, Shintaro Kazama, and fled.
Upon being rejected once more, Awano turned up the pressure on Kiryu even more; sending even more of his goons to tear up Kamurocho until they could find him and burning down his apartment. Taihei goons eventually caught Kiryu hiding out at Serena, informing their boss bout his location. After fighting his way past several waves of Taihei thugs, Kiryu was attacked by Awano and Kuze, with the intent of murdering him in the middle of the street to make an example of him. Unfortunately for them, Tachibana drove up to the scene in his sports car and rescued Kiryu from his attackers.
After Kiryu and Tachibana got in contact with Chairman Takashi Nihara of the Tojo headquarters and persuaded him to grant Kiryu a pardon, the Dojima Family was forced to call off their direct manhunt for Kiryu. This direct reproach from the Clan HQ aggravated Patriarch Sohei Dojima and thus made Awano and the Taihei fall out of favor with him. Instead, the third Dojima lieutenant, Keiji Shibusawa, would gain Dojima's favor and take control of the family's plans to take out Kiryu and acquire the Empty Lot.
After Awano is killed by Lao Gui, Kuze and Shibusawa are arrested and the Dojima Family loses control of the land for the Kamurocho revitalization project, the Taihei Association is disbanded and their members are absorbed into the Kazama Family and the main Dojima Family.