Most pet insurance companies work by reimbursing you after you pay the vet out of pocket.
So you'd take your pet to the vet, get the procedures done by the vet and then when you get the bill from the vet you pay the full vet bill out of your own pocket.
Then you make a claim with the pet insurance company and they reimburse you the money back after you make the claim.
But there are some pet insurance companies that do pay the vet directly if you search online for pet insurance that pays vet directly.
One of those pet insurance companies is trupanion pet insurance company and I have them myself and they've always paid the vet on time and directly like they said they would so I never had to pay out of my pocket and wait for reimbursement.