Your new accountant will need to complete a “64-8: authorising your agent” form to enable them to speak to HMRC directly in regards to your tax affairs.
The form contains both your details and your new accountant’s details, and will need to be signed by you.
Alternatively this can be completed online:
https://www.gov.uk/guidance/applying-for-client-authorisation-using-hmrc-online-services
I run my own accountancy business and I always complete the paperwork and just have new clients sign a paper form.
You shouldn’t need to complete anything other than the above for HMRC.
One final step will be to give your old accountant authority to pass your previous tax returns and any notes to your new accountant. However, they will contact you with their process to complete this.