William and Kate spent much of Kate's pregnancy in Anglesey, where he is based as a search-and-rescue pilot. He will give a speech and accept a gift at the farming event and meet local young farmers.
Prince William took part in the the Jerudong Trophy at Cirencester Park Polo Club on July 14
The new dad will also watch gundog and falconry displays and view some cattle judging before moving to the central show area, where he will make a short speech before being presented with a gift.
It has also been speculated that Prince William and Prince Harry will attend a charity polo match this weekend at Coworth Park in Berkshire. The park is close to Bucklebury, where Kate, William and their newborn son Prince George are currently enjoying life as new parents at the Middleton family home.
Kate Middleton pours champagne over newly-christened lifeboat 'Hereford Endeavour' in Anglesey in 2011
It has been reported that the royal couple have plans to move into their own country retreat. The new family is said to be relocating to Anmer Hall on the Queen's Sandringham estate in Norfolk, which will become their primary residence until renovations are completed at Kensington Palace.
It is understood that the Queen has asked the current tenant of Anmer Hall to vacate the property as soon as possible, four years before his lease is up. The 10-bedroom Georgian property is currently being lived in by company director James Everett and his family, who have resided there for 13 years.
This week, Everett confirmed to the MailOnline that the family timber business, Norfolk Oak, which is run from the property's stables, has already started moving out of Anmer Hall ahead of the lease, which was not due to end until March 2017. He denied that he is receiving compensation from the Queen to leave early.
It was revealed earlier this year that William and Kate had been planning major renovations for Anmer Hall. Changes approved all provide the house with greater privacy and security and include re-routing of the driveway, extensive tree planting to shield the property, and plans to expand accommodation, perhaps for the couple's protection officers.
Photos: Getty Images
A version of this article appeared at Hellomagazine.com with the headline "Prince William to attend first royal duty since the birth of his son."