Payment date - change of employer

As this occurs after the first of the month I would assume the old employer pays the May installment and the new employers picks up from June. In reality it does depend on when the old employer stopped payments.

Payment is calculated  from the last day of the month, it comes from the DAS account the employer is with on that date but see:

Stop dates to use following a change of employer where the gap in employment is 30 days or less – Apprenticeship Service Support (education.gov.uk)

HTH

It would be helpful if the ESFA could include an additional example and instructions within that article for the correct dates to use when the gap is within a calendar month, rather than straddling two months as per the only example given. It's useful for that specific scenario, as there is no employer in place on the last day of the month so the article clarifies who pays each instalment.

However if an apprentice left their original employer on 30th March, and started with a new employer on 31st March - does the new employer pay the March instalment?

It is the employer they are with on the last day of the month so if they start with the new employer on the 31^st they the funding for that month would come from the DAS account for them.