Presumably the transparency film is 135 format, if so, the simplest way is to project the image using an enlarger onto the 4x5" C41 film which is held in place using an enlarging easel.
Obviously everything is done in total darkness, so you'll need to get things in order to achieve good positioning.
You may wish to practise with B&W film first to get technique right, then move onto colour negative.
Whenever you duplicate, or transfer an image from one piece of film onto another, you will end up with a contrast kick and as transparency film is often high in contrast, this could be an issue. Kodak used to manufacture C41 duplicating film, C41 Color Print film (which is made to give you a transparency from a colour negative and used to make print film for cinema projection). Both of these were available in 135 and 4x5 format among other sizes, but no longer available today to the best of my knowledge.
You may have issues with the Tungsten light source of your enlarger giving a colour cast to the C41 colour film you are projecting onto. We actually had a colour correction filter below the lens on the enlarger for this issue. It could be possible to use filtration in the colour head.
Doing duplication work under an enlarger is fraught with dust issues, in my own darkroom I have a compressor with a water filter and a dust filter for the air. The unexposed film was placed in the easel and taped on one of the short sides, I then gently lifted the film while at the same time turning on the air to gently blow firstly underneath the film, then over the top of the film once it was flat. This did to a certain extent remove most of the dust, but within reason, never 100%.
Around once a month for around 10 years I used this process to enlarge onto 4x5" colour negative film; it was a very rewarding but sometimes quite frustrating time.
Contact printing works well, dust issues are about the same, using a vacuum easel works best. Simplest method is a sheet of glass on the top, but vacuum is better.