Which of the following scenarios would involve a tenant improvement allowance?

A tenant improvement allowance is a sum of money provided by the landlord to assist a tenant in making alterations or improvements to the leased space in order to meet their specific needs. This often occurs in commercial real estate settings where businesses require a certain layout, design, or functionality that may not be present in the existing space.

In the scenario where a tenant needs to install additional signage in a retail space, this would typically be considered part of the tenant's improvements to make the space more suitable for their business operations and branding. Signage is an essential component for retail visibility and customer attraction, hence landlords often provide allowances to help cover these costs.

The other scenarios do not involve tenant improvements. Rent reductions and lease extensions address financial and contractual terms rather than necessary alterations to the space itself. Moving expenses, while a concern for a tenant, relate to the logistics of relocating rather than improving the leased property. Thus, the most fitting scenario for a tenant improvement allowance is the one involving the installation of additional signage.