Walker is taking a career break at the end of December, having worked at Kames for eight years.
Peacock will co-manage with existing co-manager and property investment director at the group, David Wise.
Having worked with Wise and Walker previously, Peacock was at Aviva Investors since 2005, latterly responsible for the £1.2bn open-ended property fund for UK pension schemes.
When he joins in December, Peacock will report to Wise and will take responsibility for the team, which includes three assistant fund managers: Gregory Beeson, Karen Fox and Ric Tsang.
The fund will retain its active value strategy; buying quality properties with the goal of enhancing yields through activity such as refurbishments, lease extensions and new lettings.
Targeting attractively priced properties in the £3m to £20m range, the team seeks assets that are often too big for most private buyers, but too small for many bigger fund managers.
Phil Clark, head of property investment at Kames, said: “We are witnessing very interesting times in the property UK sector following the vote to quit the European Union in June. The decision has created both challenges and opportunities for the property market. Richard has worked in the property industry for almost 20 years and the wealth of experience he brings, combined with that of the highly experienced existing team, will ensure that we are well positioned to continue maximising these opportunities.”