The registration is lower tier. Lower tier covers businesses that carry only their own waste, or specific exempt categories, and it does not expire in the way an upper tier registration does.
The address held on the register is TEESDALE TYRE & AUTO CENTRE, STATION STREET, THORNABY, STOCKTON-ON-TEES, TS17 6AG. That is the address the business gave the Environment Agency, and it is not necessarily where a collection vehicle is based.
A further 6 carriers are registered elsewhere in the TS postcode area.
Whoever you use in STOCKTON-ON-TEES, the duty of care under section 34 of the Environmental Protection Act 1990 stays with you: you need the carrier's registration number and a waste transfer note for every load that leaves your premises.