When you need to apply for a full licence
You only need to apply for your full licence if:

you did not give your provisional photocard driving licence to the examiner after the test, for example because you need to use it as ID
you changed your name or address and it’s now different from the name or address on the provisional photocard driving licence
you have an old-style provisional driving licence (one issued before 1998)
Otherwise, it’ll be sent to you automatically.

How to apply
If you’re applying for a full licence, you need to:

sign the declaration on your driving test pass certificate
fill in form D1 ‘application for a driving licence’ – you can get one from a Post Office that offers DVLA services
include original documents confirming your identity
include a passport photograph (only if you have a paper provisional licence)
include your provisional licence
Send all documents to:

DVLA
Swansea
SA99 1BN

If you’re applying for a full licence by post, you must send documents to the DVLA within 2 years of passing your test or you’ll have to take it again.