You want a vet for Tigger. The first thing is to get your former vet's records for Tigger. Get hardcopy printouts for yourself. That's the only sure way you know the records have been transfered. Once you have the records, keep the original and copy it for your new vet.
Referrals are the first place to start.
A referral from your vet, from friends, from associates at work. Then you hit the phone book. A close vet is not a trivial consideration. A vet who treats cats is a must. It's my impression, sexist though it may be, that women make better cat vets than men, but I've known male vets whom I respected.