No, you do not need to serve waiting periods again for Hospital Cover if you change insurers and take out a new policy at the same level of cover as your existing policy. However if you are changing to a higher tier of cover, waiting periods will apply for the new services and treatments (known as Clinical Categories) you were not covered for previously.
If you are changing your Extras Cover policy to a different insurer, in most cases you will not need to serve waiting periods again for a policy at the same level of cover. However since Extras Cover waiting periods vary considerably between insurers, it is worth asking your insurer to confirm in writing what waiting periods will apply to you.