Error you are getting because you are creating a primary key and foreign key relationship between both the table by assigning a primary key of table as foreign key in another and vice versa. From my point of view if you want to perform this kind of operation you should simply adopt normalization feature in your DB structure.
Error you are getting because if you look at your table structure one table accepts foreign key of another table and when you try to add a record in one table your corresponding entry of primary key needs to be there in the parent table. The better approach to solve this would be
Normalize your table structure like the below.
Client(client_id(pk), first_name, last_name)
Hope that solves your problem.