The phrase "opportunity appears" is correct and usable in written English. You can use it to refer to an opportunity coming into one's life. For example: Jack was surprised when the opportunity to travel abroad appeared out of the blue.
But when the opportunity appears I consider it immoral not to take them," he replied.
Mr. Kerry's greatest opportunity appears to remain Mr. Bush's handling of Iraq.
Despite a record of 2-0-2 since Barber took over, the Flyers' window of opportunity appears to be closing.
A giant dust storm enveloping NASA's Mars rover Opportunity appears to have eased slightly over the weekend, allowing the rover to recharge its batteries a little.
Nine months later, a new opportunity appeared.
The most likely opportunity appeared to be at a UN leaders' lunch Tuesday.
Last month, the European Commission fined the company €497m ($612m) and ordered it to behave better.More specifically, two windows, so to speak, of opportunity appear to be opening.
Awesome tool! I started using it one year ago and I never had to look for another app
Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia