A further definition from The (Alternative) Legal Costs Dictionary:
Law costs draftsman n. a lawyer concerned with quantifying the legal costs of a case. A costs draftsman is to the legal profession what a train spotter is to the world of professional sportsmen. Similar to an accountant but without the glamour or dress sense.
When asked what I do, I always explain it’s like accountancy only not as exciting.
(a lawyer sic)
A law graduate who could not get a training contract or pupillage.