Richmond played finals for the first time in 12 years this season, losing to Carlton in the first elimination final.
O'Neal, an American-born lawyer who is the first woman to become president or chairman of an AFL/VFL club, said Richmond's next on-field goal was to make consecutive finals appearances, something the Tigers last achieved in 1971-75.
But asked whether Richmond, whose 10th and most recent premiership was won in 1980, could add another within the next five years, O'Neal was hopeful it wouldn't take that long.
"We're hoping for a premiership in the next year, in the next two years," O'Neal told Melbourne's 3AW radio.
"But we see that as definitely on our horizon, our short-term horizon.
"What we're really trying to do is restore Richmond to the position of significance in the AFL and the broader community that it's enjoyed in the past and we want to see that as its future as well."
O'Neal was voted in on Thursday ahead of fellow board members Malcolm Speed and Maurice O'Shannassy, replacing Gary March, who was president for eight years.
O'Neal said being the only woman in a room full of men at meetings with fellow club presidents would be nothing new for her, given her legal background.
But she said she had never encountered sexism in the AFL and had received support from all quarters since her appointment.
"It's been delightful the outpouring of support I've received from the other club presidents just in the past few hours, as well as from the AFL and our members and supporters," O'Neal said.
"One of the big challenges for me will be returning all the calls and getting through the emails.
