A safety expert was someone who ensured that a dangerous activity was performed safely.
In 2373, while preparing to descend into a cave to look for gallicite, B'Elanna Torres suggested bringing Tom Paris along for his rock climbing expertise. When Vorik mentioned his own experience, having explored the Osana caverns, known to be perilous, over many summers, Torres suggested the two officers could be the away team's safety experts. (VOY: "Blood Fever")