I haven't heard 'do the need be', but it could be like 'do the needful', which was used in the nineteenth century but has fallen out of use in modern British English, though is still found in South Asian English. It's certainly not a phrase I would use.
In a letter, I generally use 'Thanking you in advance, I look forward to hearing from you.' then put the 'Yours sincerely' underneath.
- For Teachers