If you are being employed as a PA then you should receive a Statement of Employment Particulars (known as a contract of employment) or, if you are self-employed, then you may choose to provide some written details of the work you've agreed to do.
This is a formal document that sets out the conditions of employment. If you are likely to be employed for 1 month or more, then you should receive the Statement of Employment Particulars within the first 2 months of your employment. However, it is often common to receive this document at the beginning of your employment so that you can agree to the terms before you start the role.
It is your employer's responsibility to draw up the Statement of Employment Particulars and the document must include particular information such as your name, their name, the hours you'll be working, place of work, etc. The following link will take you to the GOV.UK's website which sets out what your employer needs to include in this document.