It's questions like these that make me wish they would've made TLK a bit longer.
What happened durring his rule you asks.
Well...
I think after Scar took the throne he made Kula, his daughter, the princess and betrothed her to Chumvi(which explains why he's still alive even though he's a threat to the throne.) Even though Mheetu is Scar's firstborn son. Chumvi mocks Mheetu about this and Kula lets him, not inclined to defend her younger brother. The only one who can actuall tolerate Mheetu is Tama and the two become friends. They sneak off to the elephant graveyards to explore and they find some hyenas are planning to rebel against Scar. Mheetu tells Scar abour this and the rebels are killed. Afterwards Mheetu request to be the heir as when the rebels were being destroyed they had claimed the lives of Kula's mother(Inalu) and Chumvi's mother(Saka) they both lose the will to rule. Scar refuses and ends up hurting Mheetu when his son refuses to take no as an answer. Mheetu ends up with 3 Scar's across one of his eyes but until Scar can do further damage the lionesses are ready to protect him.
The death of his queen and the distrust of the lionesses(and even some of the hyenas) have left him without a queen and his daughter's deminishing desire to become queen has left him heirless. He decides to visit an old friend who helped him murder Mufasa's firstborn son, Mosi(who is mine), Amri(who is also mine) but when he get's there he finds Amri has just passed on. The leadership passes on to his daughter, Zira. Onces Scar's sees this his original plan, which was to offer Amri a place beside him to help him rule and keep order with the lionesses and hyenas. Instead he offers Zira the chance to come to the pridelands and live there if she promises eternal loyalty and having no previous leadership skills, Zira accepts. Months pass and during these months Zira and Scar have produced Nuka.
*will update later*