No – you don’t need a director’s fee as you can potentially utilise your personal allowance to offset against income taxed at source by the umbrella company paying you.
The main reasons to process a director’s fee is to utilise your personal tax allowance efficiently( if you have no other employment income or pension income), benefit from corporation tax relief on this payment and ensure that you making adequate credits towards your state pension.
If you are working through an umbrella company for the full tax year, then no funds are paid to your limited company and it is generally more tax efficient to utilise your personal allowance against umbrella income which is taxed at source.
If there are no profits in your PSC, then the provision of a director’s fee as an additional company expense would not provide any further tax relief in the accounting period. In addition, NI credits are still being maintained to your state pension via NI deductions from your umbrella employment income.