Once you pass your driving test, the examiner will typically take your provisional driving licence, and arrange for the DVLA to send you your full licence. You can still drive while you wait for your full licence to arrive, however. You just need to make sure you are carrying the driving test pass certificate you are given once you complete your exam.
If you didn’t hand over your provisional licence, for example if you need to use it as ID, then you have to fill in a D1 ‘application for a driving licence’ form. This can be downloaded from the DVLA online, or picked up at the Post Office. You will then need to send the following to DVLA, Swansea, SA99 1BN:
your completed D1 form
your signed driving test pass certificate
original identification documents
a passport photo (if you have a paper provisional licence)
your provisional driving licence
You may also need to apply for a full licence by post if you have changed your name or address, and it is different to your provisional licence.