you have two options to solve this problem:
EASIER BUT LESS FLEXIBLE: creating an Airtable automation that gets triggered when a client record column is checked. The action for that automation should be to look for all the records in the tickets table that are related to the client record. Then you can add an update action to change the status of all those records.
MORE COMPLEX BUT MORE FLEXIBLE: creating an Airtable automation with a script that also gets triggered when the checkbox is checked. The script looks through all the tickets records and finds all the tickets that are connected to the client. It then can perform different actions on them such as:
Hope this helps!