In Singapore and some Middle Eastern countries, you can hire a maid on local transfer, direct hire from other countries or through an agency.
To hire a maid on local transfer, the maid must have a declaration form (in Singapore) or a no-objection certificate (NOC, in Middle Eastern countries) provided by her current employer. If the current employer does not agree, the domestic worker will have to return to her home country.
This will be considered as overseas hire and you must use an agency for paperwork processing. Overseas hire also includes direct hiring a helper who is in her home country or working in another country.
When the current employer does not agree on the transfer, it may be worth asking the helper for her employer’s contact details, since talking to them directly may help and your maid might be able to start her job sooner.