It's the holding which has the TB Testing time period, not the animal.
Depending on where you are in England and the local approach to TB, which is now risk-based, and the same for the destination holding, you may or may not need animals tested before they are moved to another holding.
I'd just ask the abbatior or your local animal health, to be sure. There are so many regional and localised variations in how it's handled now, unless one of us is in the same parish as you we probably don't know the rules which apply to you. And even then, we might be wrong, as some of the restrictions can be applied to individual holdings, and to holdings which abut holdings on which there has been a reactor, and not to other holdings in the same parish.