There is understood to be a wider reorganisation in progress at HS2 Ltd, which is responsible for planning and building the mooted high-speed rail link from London to the North.
It is not yet clear how Leeks’ responsibilities will be divided.
Andy Taylor, who joined in May, remains in place as head of public affairs.
The legislation paving the way for the first part of HS2, a line from London to Birmingham, is in the process of going through Parliament.
HS2 said in a statement: "In Clinton's time at HS2 he has led a national consultation and engagement programme that had seven separate public consultations and six rounds of 24 community forums, along with an intensive series of meetings with local authorities, NGOs and businesses.
"This unprecedented effort for a public project has set a solid foundation for the parliamentary phase. Clinton will be continuing to work as he has for the past 25 years on major infrastructure projects, in the UK and Asia."