Yes, under certain circumstances. Many approved shotgun clubs and Registered Firearms Dealers hold open days, where people without certificates can fire club guns to test their interest in the sport.
The club or dealer must hold a section 11(6) permit, issued by the police, which allows these events on a limited number of days each year.
Approved rifle and muzzle-loading clubs will allow the shooting of club guns providing you are a club member. Clubs also allow non-members to use club weapons on a limited number of days as guests.
You may also shoot shotguns and rifles when accompanied by a certificate-holding landowner or their agent, such as a game warden. You must, however, shoot on the owner's land, using their weapons within the limitations of the certificate for that weapon.
You may not borrow another person's gun if they do not occupy the land you intend to shoot on.