The phrase "after defying a request" is correct and usable in written English.
It can be used when describing an action taken following the refusal to comply with a specific request.
Example: "She decided to proceed with her plan after defying a request from her supervisor to hold off on the project."
Alternatives: "after rejecting a request" or "after refusing a request".
On Monday, he took a last measure of satisfaction by defying a request of the K.G.B. agent who had escorted him on the plane from Moscow to East Berlin.
WikiLeaks supporters initially mobbed courthouses over the course of six acrimonious hearings, chanting, "We love you, Julian," when Mr. Assange was denied bail as a flight risk and briefly jailed in December after defying a judge's request to provide an address.
In August 2015, I succeeded in reaching Europe after defying a travel ban imposed on me by the Iranian regime.
A number of Japanese journalists were reported to have been arrested after defying a cordon at the hospital.
A11 Protest Violence in Ivory Coast Youth leaders urged their supporters to abandon their deadly protests after thousands of young people defied a request from the president of Ivory Coast to end days of rioting and violence.
The ruling came after a dramatic and gruelling late-night session broadcast live on television and across news sites, and defied a request from the United Nations human rights committee that he be allowed to stand.
Bank of America on Monday defied a request by Representative Edolphus Towns, Democrat of New York, to divulge more details about the star-crossed acquisition.
But relations between the BMA and the Government suffered another blow as the union told striking medics at a Birmingham hospital to defy a request to return to work.
On Monday, thousands of Kuwaitis defied a request by the authorities not to participate in the anti-government demonstration in Kuwait City.
Since the couple married, the British press has generally fallen in with informal requests by their office for privacy, although The Sun, a Murdoch-owned tabloid, defied a royal request to refrain from publishing the photographs of the naked Prince Harry after they appeared elsewhere.
