In the event, she isn’t pregnant or you breed her again next year, typically people do one of two things. Find a registry you want to work with (based on customer service, nearby inspections, lots of horses in discipline, etc) and have her inspected for that registry and then use stallions that are approved by registry (or if registry allows outside stallions to be used, you can do that) or find the stallion(s) you want to breed and have her inspected by a registry he’s approved by (this method may result in having to get multiple mare approvals over the the years).
I guess there is a 3rd option that some people to…say “you don’t ride papers” and just breed to whatever stallion you want to and don’t get papers.
Some registries are easier to get TB mares approved with. RPSI and ISR/OldNA are both known to be TB friendly. AHS is probably the most difficult to a TB mare into. The others are open to good quality mares.
Hope that helps a little.