I don't know in terms of timescales, however you won't need to transfer the extension into your name per se.
I suspect the original lease is actually being surrendered and the new extended lease granted on the same terms (albeit presumably with some variations re ground rent and other clauses which may need updating or which the landlord wishes to include). Thus, when you complete and acquire the title of the property you will become the lessee of the new lease (albeit the name of the lessee of the physical lease will always be the seller from whom you are buying).
If you wish, I can point you in the direction of names / firms who will be able to advise further - whereabouts are you buying?
Incidentally, this isn't an extension which has been caught up in the Leasehold Solutions / Leasehold Valuers liquidation is it?
Posted By: NxNW, Jun 1, 12:15:29
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