The real way of establishing the Khilafa
The Islamic Khilafa will have to be established according to the Sunanh of the Prophet sallallahu alayhi wasallam, based upon Shurat of the Muslims and with the consent of the majority of Ahlul Hal Wal-Aqd.
As for restricting this term "Ahlul Hal Wal Aqd" to ones own group such that whoever agrees with them is from the Ahlul Hal Wal Aqd and whoever disagrees is not from them, this is straying from the way of the believers.
Umar radiallahu anhu said: “If a man takes Bay’at without consulting the Muslims, then there is no Bay’at to him and those who gave their Bay’at are required to change him or kill him.” Narrated by al-Bukhari
Sheikhul Islam Ibn Thaymiyya rahimahullah said: “If it was that Umar and those with him gave Bay’at (to Abu Bakr al-Siddiq) but the rest of the companions did not, then he would not be an Imam by that. But rather he became the Imam only after the majority of the companions gave him the Bay’at.” Minhaj al-Sunnah 1:530
And he also said: “When the people of might and strength gave Bay’at (to Uthman), he became the Imam. If for example Abdur-Rahman ibn Auf gave him the Bay’at but Ali and the other companions who are the people of might did not give him Bay’at, he would not be an Imam.” Minhaj al-Sunnah 1:533