There is no overriding or insurmountable legal impediment to an individual simultaneously being the chair of the board of more than one trust.
For foundation trusts paragraphs 8, 16 and 17 of Schedule 7 of the National Health Service Act 2006 as amended by the Health and Social Care Act 2012 (the amended Act) apply. These specify that a non-executive director (NED) and the chair must be eligible to be a member of the patient or public constituency of the membership and that the person must not be disqualified from being a director under the provisions of paragraph 8 of Schedule 7. The amended Act specifies that it is for the council of governors to appoint the chair.
NHS England and Improvement, in its role of Monitor, has the power to remove foundation trust directors including the chair where the trust is in breach of its licence and the circumstances warrant it. It also has the power to direct the appointment of an interim, but there is no power to impose a particular replacement on the foundation trust.
The directors of foundation trusts, including chairs, also have a duty to avoid a situation in which the director has (or can have) a direct or indirect interest that conflicts (or possibly may conflict) with the interests of the corporation (foundation trust) and a duty not to accept a benefit from a third party by reason of being a director or doing (or not doing) anything in that capacity. Chairs of trusts and foundation trusts must also meet the requirements of the fit and proper person test.
For NHS trusts, the National Health Service Trusts (Membership and Procedure) Regulations 1990 apply. Until quite recently these regulations prevented NHS trust chairs from also chairing foundation trusts simultaneously, but the regulations were amended in 2014 to remove these impediments. These regulations empower the secretary of state to appoint and by implication remove the chair of NHS trusts, but this power is delegated to NHS Improvement.