Trekking will represent the global operation for the third year running in Saturday's $15 million feature, while Kementari lines up for head trainer James Cummings in the Group 3 Sydney Stakes (1200m).
Godolphin had been mulling over running one of its band of top colts – Anamoe, Paulele and Ingratiating - in its Everest slot and Cummings revealed they came very close to selecting last weekend's Roman Consul Stakes winner Paulele.
But in the end, Trekking's experience won out.
The last-start Moir Stakes placegetter has performed admirably in two Everest appearances, motoring to the line for third behind Yes Yes Yes in 2019 and again prominent when fourth to Classique Legend last year.
"He was really brave in two attempts at the race already and it tells us he copes with pressure," Cummings said.
"I think he's going well enough third-up with the Moir (Stakes placing) next to his name. It's good enough form for him to be a competitive chance."
Kementari is among the reserves for The Everest (1200m) should a slot runner be scratched and while Cummings hasn't ruled out a belated call-up, his focus is on the Sydney Stakes.
The seven-year-old has been a hard horse for punters to catch throughout his career but he is a cherished member of the Godolphin team.
He heads into Saturday's race after getting his nose in front to score a first-up win in the Gilgai Stakes at Flemington, with Cummings' only query a potentially heavy track at Randwick.
Kementari hasn't missed a place in four starts on soft ground but is unknown on anything worse.
"He's the type of horse, when he gets up and wins, he gets a lot of emotion out of the entire Godolphin operation," Cummings said.
"He was fantastic down the straight first-up. He beat Zoutori, who's a Group One sprinter in his own right (and) the winner of a Newmarket.
"He can win the Sydney Stakes but he's never seen a heavy track in his career."
Trekking was a $34 chance for The Everest with TAB fixed odds on Thursday with Kementari on the second line of Sydney Stakes betting at $4.60.