Ali Mirza Safavi
Ali Mirza Safavi also known as Soltan- Ali Safavi( died 1494) was the penultimate head of the Safavid order.
Having grown wary of his political power, Ali Mirza was captured by the Ak Koyunlu and spent several years in captivity in Fars before being released in 1493 by prince Rostam.
In the ensuing period he and his men assisted the prince in defeating Baysonqor bin Yaqub.
A year later however, in 1494, now perceiving the Safavid order as a threat to his own position, Rostam ordered for the execution of Ali Mirza Safavi.
Realizing his inevitable fate, shortly before his death, Ali Mirza Safavi appointed his brother Ismail as his successor.
Ismail, in turn, eventually came to establish the Safavid Empire, with the regnal name Ismail I( 1501 – 1524).
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Abd al-Muttalib
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Haydar Mirza Safavi
Haydar Mirza Safavi (also spelled Haidar Mirza Safavi) was a Safavid prince, who declared himself as the king (shah) of Iran on 15 May 1576, the following day after his father Tahmasp I had died.
He was, however, during the same day killed by the Qizilbash tribes that favored his brother Ismail Mirza Safavi as the successor of their father.
His mother was Sultanzadeh Khanum, a Georgian lady.
Kaya Alp
Kaya Alp was, according to Ottoman tradition, the son of Kızıl Buğa and the father of Suleyman Shah, who was, in turn, the grandfather of Ertuğrul, and the great grandfather of the Ottoman Empire founder, Osman I.
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Tahmasp I
Tahmasp I  (22 February 1514 – 14 May 1576) was an influential Shah of Iran, who enjoyed the longest reign of any member of the Safavid dynasty.
He was the son and successor of Ismail I.
He came to the throne aged ten in 1524 and came under the control of the Qizilbash who formed the backbone of the Safavid Empire.
The Qizilbash leaders fought among themselves for the right to be regents over Tahmasp, and by doing so held most of the effective power in the empire.
Upon adulthood, however, Tahmasp was able to reassert the power of the Shah and control the tribesmen with the start of the introduction of large amounts of Caucasian elements, effectively and purposefully creating a new layer in Iranian society, solely composed of ethnic Caucasians.
This new layer, also called the "third force" in some of the modern day sources, would be solely composed of hundreds of thousands of ethnic Circassians, Georgians and Armenians, and they would continue to play a crucial role in Persia's royal household, harems, civil and military administration, as well as in all other thinkable and available positions for centuries after Tahmasp, and they would eventually fully eliminate the effective power of the Qizilbash in most of the functioning posts of the empire, by which they would also become the most dominant class in the meritocratic Safavid kingdom as well.
One of his most notable successors, the greatest Safavid emperor, Abbas I ("also known as Abbas the Great") would fully implement and finalize this policy and the creation of this new layer in Iranian society.
Tahmasp's reign was marked by foreign threats, primarily from the Safavid's arch rival, the Ottomans, and the Uzbeks in the far east.
In 1555, however, he regularized relations with the Ottoman Empire through the Peace of Amasya.
By this treaty historical Armenia and Georgia were divided equally between the two, the Ottoman Empire obtained most of Iraq, including Baghdad, which gave them access to the Persian Gulf, while the Persians retained their former capital Tabriz and all their other north-western territories in the Caucasus (Dagestan, Azerbaijan) and as they were prior to the wars.
The frontier thus established ran across the mountains dividing eastern and western Georgia (under native vassal princes), through Armenia, and via the western slopes of the Zagros down to the Persian Gulf.
The Ottomans, further, gave permission for Persian pilgrims to go to the holy places of Mecca and Medina as well as to the Shia sites of pilgrimages in Iraq.
This peace lasted for 30 years, until it was broken in the time of Shah Mohammad Khodabanda.
Tahmasp is also known for the reception he gave to the fugitive Mughal Emperor Humayun as well as Suleiman the Magnificent's son Bayezid, which is depicted in a painting on the walls of the Safavid palace of Chehel Sotoon.
One of Shah Tahmasp's more lasting achievements was his encouragement of the Persian rug industry on a national scale, possibly a response to the economic effects of the interruption of the Silk Road carrying trade during the Ottoman wars.

Question: Who is Haydar Mirza Safavi's paternal grandfather?
Answer: Ismail I