A good place to start would be the UAL images library guide which you can find here: arts.ac.libguides.com/images 

The 'Image Resources' tab provides a number of links to online image archives, databases and resources. Bridgeman Education and Britannica Image Quest are good starting points for general image searching. The 'Finding and working with Images' tab has help with search terms as well as links to image search engines and copyright information.

The guide also features contact information for librarians at each site who can help you if you have any further questions. 

Specifically for Catwalk and fashion show images you could look at these Databases listed below, which are all accessible from the Databases A-Z list (the link to this page is on the right-hand side of the library search page). 

firstView - for images of collections on catwalks, browse by designer. 

Bloosmbury Fashion Video - videos of catwalk shows mainly from the late 1980's-early 2000's. 

WWD - includes some image collections of shows if you search by designer.