The phrase 'trek of' is not correct or usable in written English.
However, you could use the phrase 'trek of [something]' in written English. For example, "We went on a two-week trek of the Appalachian Trail."
From Rafu to our proposed evening camp would be a trek of 30km.
The disastrous transcontinental trek of President Warren G. Harding still looms large.
In the case of Star Trek (of which — dare I admit?
This would be a linear trek of about 50km over two days.
"Star Trek," of course, gave birth to four separate series, but those were all spinoffs.
The "great trek" of this first Cornish contingent was a combination of the epic and the absurd.
But the refugees will not forget this trek of Biblical proportions of which they are a part.
From Ghangria, the Valley of Flowers is a rigorous trek of nearly four miles, past enchanting waterfalls and glaciers.
It would be a yearlong trek of about 2,000 miles layered with danger, privation and violence.
The trek of the Cherokee in 1838 39 became known as the infamous "Trail of Tears" (see Cherokee).
Take bus 21 to Marseille University's Luminy campus for a dramatic and strenuous trek of over an hour.
