In order to remain part of Open Banking these EEA participants will need to ensure that they have made a Temporary Permissions Regime (TPR) notification to the Financial Conduct Authority (FCA) by 11 April 2019.

In the event of a no implementation period when the UK withdraws from the EU, the UK will be deemed a ‘third-country’ by the latter, meaning EEA firms will no longer be able to passport into the UK. The TPR was created in 2018 by the FCA to help firms that passport into the UK (including banks, payment and e-money institutions) to continue operating if the passporting regime falls away abruptly during this period.
What you need to do

As an EEA firm, you will need to notify the FCA of your intention to apply under the TPR by the date specified above. This will give you permission on a temporary basis, reflecting your passporting permission pre-Brexit. This permission will be in place for a maximum of three years within which time you will be required to obtain authorisation or recognition in the UK.
Consumer Protection

Firms will be expected to comply with FCA requirements from Day 1 in order to maintain an adequate level of consumer protection. For more information please refer to the dedicated FCA page on the TPR .
How To Apply

A TPR application can be made via the FCA Connect service. The User Guide link is below:

https://www.fca.org.uk/publication/systems-information/temporary-permission-notification-connect-guide-funds.pdf

NB: Treatment of Gibraltar-based firms is unchanged.