Esonica has been a top model in St. Thomas since the age of 9, beginning with the Roses and Champagne Agency. She has participated in many other fashion events including the Face of Shabeau in Barbados, winning the coveted cover model spot, and the Caribbean Fashion Week Catwalk held annually in the Virgin Islands. Her big break was in 2007 when she joined America's Next Top Model. She made the first cut during the casting call auditions in Montgomery, Alabama. She was also a finalist in the singing competition V.I. Idol in 2008.
Pageantry
Esonica’s successes on the local and international level includes winning the titles of Ms. Hal Jackson’s Virgin Islands Talented Teen 2005, Ms. Hal Jackson’s International Talented Teen 2005, Ms. America’s Outstanding Teen Talent Winner 2006, and Virgin Islands Carnival Queen 2007. Esonica was selected as one of "The 50 Most Beautiful Women in the World” by a panel of judges for Global Beauties. A panel of international judges made their selection based on the top international pageants held worldwide in 2011.
Miss World 2011
By achieving the first runner up, Esonica became the country's representative for the 2011 edition of Miss World. She finished as part of the Top 15 semifinalists. During the fast track events, Esonica placed as part of the Top 36 for Beach Beauty round, second place for the talent round, and part of the Top 20 for the Beauty with Purpose segment. The pageant was won by Ivian Sarcos of Venezuela.
Miss Supranational 2013
In May, 2013, Esonica was crowned Miss US Paradise Supranational, and traveled to Minsk, Belarus, where she represented the US Virgin Islands in the Miss Supranational Pageant. Esonica was awarded second runner Up in the Talent Finals, and placed fourth Runner Up in the Grand Finale, making her the first representative from the US Virgin Islands to place in the Top 5 of an International Pageant. The pageant was won by Mutya Johanna Datul of the Philippines.
Miss Earth 2014
Esonica flew to the Philippines in November 2014 to compete with almost 100 other candidates to be Alyz Henrich's successor as Miss Earth. She did not place in the competition but was awarded as Best Teacher and Best in Talent.
Miss Universe 2017
Veira represented the U.S. Virgin Islands at Miss Universe 2017 in Las Vegas, Nevada.
Reality Television
Esonica appeared on Season 2 of Temptation Island, an American reality television program broadcast on USA Network in which Esonica, along with her boyfriend, was one of several couples who agreed to live with a group of singles of the opposite sex, in order to test the strength of her relationship.