To adjust the derailleur, look at the point where the cable enters the rear derailleur in the photo. See that black round knob-like piece where the arrow is pointing? That's a barrel adjuster, which is used to tune the derailleur adjustment.
Standing behind the bike, the barrel adjuster is turned either counter-clockwise or clockwise in half-turn increments until the shifting hesitation is cured. Which way do you turn it? It depends on what type of hesitation you're experiencing. The most common problem is slow shifting into easier gears (toward the spokes) due to the cable stretching. But, it's possible that you're experiencing the opposite.
This rule will help you remember which way to turn it: If the derailleur is hesitating when shifting toward the spokes (the more common problem), turn the barrel toward the spokes (counter-clockwise); and if it hesitates shifting away from the spokes, turn the adjuster away (clockwise) from the spokes. (Always turn it only a half turn, shift multiple times to check the adjustment, and repeat as needed to cure all hesitation.)
Protect That Derailleur
What Are Those Little Screws For?