The most important way by which vets contribute to vaccine development is by serving as primary test subjects for the vaccines. All good vets will test vaccines on themselves before they try them on their patients. Human models of disease have become increasingly popular in recent years, as they reliably replicate animal diseases, creating important avenues for the future development of life-saving veterinary drugs.
Similarly, as per
this veterinarian's website detailing proper procedure for choosing appropriate dental chews for canine patients, "If you hit your self in the knee with the object and it hurts, it’s probably too hard/heavy for your dog."
(But actually - I would assume they're looking for a) some vets go into research and might directly develop or test different recombinant vaccines in the lab, b) clinical testing, c) more broadly, by helping to collect and report data that can be used by researchers to know which vaccines they should be working on, which might be good candidates for recombinant gene editing, etc)