It's in geosynchronous orbit.
How will Coriolis Effect be a factor?
Please elaborate.
As you say, it is geosynchronous, by definition, because it is tethered.
If the outer space end is 69,000 miles out, it will have an orbital (call it "horizontal") velocity of about 41,000 miles per hour. (Well above escape velocity, by the way, if the tether ever breaks!)
A load starting up the tether from the surface of the Earth starts out having a maximum horizontal velocity of about 1,000 miles per hour.
The load must accelerate horizontally to achieve a horizontal velocity proportional to its distance up the tether.
There is no way the tether can impart any horizontal acceleration (to counteract this coriolis force) except by bending like a drawn bowstring.
If the load has not reached synchronous velocity by the time it reaches the upper end of the tether, it will simply wrap the tether around the Earth like a line on a fishing reel.
In short, a rocket assist is probably what's needed, which defeats the entire purpose of the "space elevator" concept.