"To start the counter" means to begin measuring or counting something. It often refers to initiating a timer or tallying system to track the passage of time or keep count of something. Full definition
Have you ever seen giroud sell a defender the dummy and score Have you ever seen giroud start a counter attack from inside our box and get at the end of it to score. (justarsenal.com)
His role is break up play and start counters at rapid pace. (justarsenal.com)
This means that they don't actually have to see each other to start the counter conditioning process. (themoderndogtrainer.net)