Local Solutions to End Homelessness Act of 2021 This bill reallocates to urban counties, under certain circumstances, Emergency Solutions Grant funds to help individuals and families regain permanent housing after experiencing a housing crisis or homelessness. Currently, the Department of Housing and Urban Development typically reallocates the funds to the state in which a city or county is located if the funds going to a recipient metropolitan city or urban county are less than a specified amount. The bill generally maintains this reallocation arrangement but also establishes certain circumstances when these funds must go to the urban county in which a recipient metropolitan city is located or to the recipient urban county directly. An urban county receiving reallocated funds designated for a recipient metropolitan city must spend these funds for the benefit of the metropolitan cities located within the county.