Create relationship between two tables that do not have unique values

one more attempt... see which of these measures work for your scenario.

Measure 3 = 
var _l = SELECTEDVALUE(Targets[Location ID])
var _FY = SELECTEDVALUE(Targets[Target Fiscal Year])
RETURN CALCULATE(
        count( Client_Locations[client id]) 
        , Filter(Targets, Targets[Target Category] = "Client Starts" )
        , Client_Locations[location ID] = _l
        , Client_Locations[start fiscal year] = _FY
)

Measure = 
CALCULATE(
        count( Client_Locations[client id]) 
        , Filter(Targets, Targets[Target Category] = "Client Starts")
        , TREATAS (
            SUMMARIZE(Targets, Targets[Location ID], Targets[Target Fiscal Year])
            ,  Client_Locations[location ID], Client_Locations[start fiscal year]
            )
)

You are doing is common scenario when you have multiple fact tables and getting related counts based on business needs.