Cook joined the company in March 2018 as a single strategy sales manager in London. He was previously at Franklin Templeton and JP Morgan Asset Management.
In his new role, Cook will report to Liontrust's head of global distribution Ian Chimes.
As part of the UK sales team restructure, the single strategy and multi-asset teams will be combined, with each person being responsible for a broader range of products, promoting both single strategy and multi-asset funds and portfolios.
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Ian Chimes said: "Our focus is continually on providing outstanding service for clients. We have evolved the structure of the UK sales team to ensure we can meet the changing requirements of the client base.
"The appointment of Kristian as head of UK distribution reflects his substantial contribution to our sales over the past few years and great relationships with clients. He will be leading a very knowledgeable team with the determination to deliver for our clients."
Cook added: "The changes for the UK team are a simplification of the UK sales model and will enable us to have more collective and individual clarity of responsibilities. With more clarity, we can be more focused, and with more focus we can get better outcomes for our clients."