Also, our University had to introduce new policy of charging for students' pick up service at the airport as our insurance requires greater liablity. 主要是这句不知道什么意思: as our insurance requires greater liablity.
liability, in insurance terms, means the coverage that you are liable to. For example, if you have a car and have a liability insurance of $50k, your insurance company will pay up to $50k to cover the damage the other party, if you are involved in a car accident
Your post doesn't provide enough context, so there is no way to tell what kind of liability is.....