I have a set of 4 DEMs for a study area however they don't overlap they only meet at the edges.
How do I collate the 4 into 1 DEM raster that I can then use to convert into contours and slope representation?
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Use the Mosaic to New Raster tool in the Data Management toolbox. This will accept your four DEMs as input and merge them together into one.
From there you will need the Spatial Analyst extension to create contours and calculate slope.
Try using production contouring. You do need an extension for it, but if you have it this can be a viable option.