Clarke, who now plays his golf on the Champions Tour, is extremely frustrated along with the rest of the golfing world at the pace of play that is consistently witnessed on Tour.
"Just give them (penalty) shots," Clarke told Reuters. "The guys that are slow give them shots and then all of a sudden they will figure out a routine where they can hit it within the limit.
"It will stop in one week if they start giving out penalty shots. It is the bad side of our sport and we need to address it."
Bryson DeChambeau has been the biggest culprit of slow play in recent weeks on Tour.
DeChambeau was seen taking two minutes and 20 seconds over a 10-foot putt during the Northern Trust, shortly before taking more than three minutes to pace out a 70-yard wedge shot.
It even resulted in Piers Morgan racing onto Twitter to claim DeChambeau "should quit" playing golf if he was not able to speed up.
Teeing up in the penultimate group alongside Holmes at Royal Portrush, the World No.1 was infuriated by his playing partner's pace of play. After leaving the 12th green, Koepka looked at the walking official in his group and pointed at a non-existent wrist watch.
“It was slow, but it wasn't that bad for his usual pace. I thought it was relatively quick for what he usually does,” said Koepka, who finished the week nine strokes behind eventual Open champion Shane Lowry.
Other deliberate players on Tour include include Patrick Reed and Patrick Cantlay, but there are also many more out there as Edoardo Molinari recently disclosed from a European Tour document.