Depends on whether taking out a new policy has any affect on the cover. If your pet has any pre existing medical issue, the new policy won't cover it. Also does your pet meet the qualifying conditions for a new policy.
Don't rush into arranging a new policy instead of renewing the old, without checking of any consequences.
My personal opinion on Pet Insurance, is that some of the policies offered by vets are more reliable when you need to claim. Because the vets practice deal with all the paperwork, it can be easier. With policies available directly with Insurers, in the event of a claim, it can be a hassle.