457b and Pre retirement catchup

[Guest Pension Girl]

What happens if an individual works for City A for X years and does not defer the maximum, then terminates with CIty A and goes to work for City B. CIty B has a 457b plan and the employee who is age 62 and 3 years before NRA under this plan wants to participate and defer the maximum - $16,500 plus unused limits - unsused limits from the prior employer plan or just this new plan (obviously there are no unsused limits as he was just hired)

Thanks!