If I have asbestos removed outside do I need a certificate to say it has been removed correctly and it is safe to carry out work or live in that area?

Further clarification would be required, for example the location of the work, the task being carried out and the type of asbestos.

This would help understand if this work would be Non-Licensed or Licensed work.

For example, if this was a shed or garage roof, this would be Non-Licensed Work and a certificate is not mandatory, but you would expect to see a self-certification from the company to show that the area has been thoroughly cleaned and visually inspected to make sure there were no visible traces of dust or debris. See page 2 on this EM10 document from HSE as an example. UKATA also provide a document that companies are free to use: https://www.ukata.org.uk/library/ukata-guidance/statement-of-cleanliness/

If the work is licensable then a certificate is required.