There are four recognised ways of competitively selecting an artist, with associated pros and cons. However, you may find other routes including through developing partnerships with arts organisations, or via existing relationships.
Finding the appropriate way to select an artist will depend on the resourcing available and the kind of project. Some selection processes judge submissions through previous work and others allow you to judge through both this and new proposals responding to the opportunity.
Examples in London include the process for the Fourth Plinth commission, which is an invited competition supported by an arts panel, arts management, and informed by public consultation. A commission for developer British Land Plc at Triton Square used specialist arts expertise and the process of direct invitation. Swiss Cottage Children’s Library within London Borough of Camden used the process of competitive interview to select a suitable artist to work closely with the design team. An open competition has recently been used by the Olympic Delivery Authority for a commission for the bridges in the Olympic Park.