These individual therapy sessions, funded by the CofE's Racial Justice Unit, will be conducted by professionals specialising in "social justice and therapeutic healing".
It adds: "We recognise the burden of racial discrimination, micro-aggressions, and systemic injustice and how heavily this can weigh on your mental and emotional wellbeing, especially as you strive to lead others."
The Church of England has been criticised in recent years for its efforts to promote diversity, equality, and inclusion.
Detractors have labelled the initiatives "anti-Christian" and a "self-destructive move" for the Church.
Controversy arose when the Church revealed plans for a £100million fund to make amends for its historical ties to slavery and address the "lasting impacts of enslavement".
This follows the Church's recent job posting for a "Head of Racial Justice Priority", offering a salary twice that of a typical vicar.
The creation of a "racially just church" is being driven by the Diocese of London.
Their position offers an annual salary of £66,646, which is almost twice the £31,644 earned by parish priests in the diocese.
The new pilot therapy programme will provide up to six sessions for seven clergy members, with the diocese planning to seek additional funding if the initiative proves successful.
Bishop Jeremiah said that despite the diocese being "one of the most diverse in the country," he had "far too often" heard of clergy experiencing harm or being let down "due to the colour of their skin".
He added: "This trial is a landmark first step forward for the diocese, and I pray that clergy within London and beyond who have been affected by racism can find support, healing, and the continued strength to fight for change."