Build and use your network
Not all UN consultancies are publicly advertised, particularly those below a certain budget threshold that do not require an external bidding process. To find such rare opportunities, you will need to build and use your network.
Contact those who might be aware of consultancies in your area of expertise. For example, if you are completing an internship with the UN, mention your interest in a consultancy to the contacts you have made during your internship.
Also use LinkedIn, Facebook and other social media channels to connect with people in your area of expertise or at the organisation you are interested in.