Other answers have great suggestions for how to give non-combat challenges to Aarakocra players. However, many Aarakocra players use a tactic in combat where they'll fly just at the edge of a weapon's range limit. They'll fly into range, shoot their weapon, and fly back out of range. This is obviously limited to certain conditions, but in an open terrain fight without proper counters, this can remove any sense for danger for that player and unbalance fights.
Ranged weapons and readied attacks
The simplest method is to have a few enemies with ranged weapons that take the Ready action on each turn. They would ready the Attack action, with the trigger being "when the Aarakocra flies within range". This does consume their reaction as well, but I find that my players usually don't risk opportunity attacks, so my NPCs rarely get a reaction anyways. This allows your ranged enemies to shoot the Aarakocra player as effectively as the player can shoot them. You should use this tactic frequently
Occasionally use spells or other effects
One single arrow, empowered by Ensnaring Strike, can send a flying creature hurtling to the ground. If they've been hovering just out of longbow range, they're going to be 150+ feet in the air - that's 15d6 fall damage. Similar effects that restrain, incapacitate, or inflict the prone condition can drop flying creatures out of the air, inflicting very heavy damage.
One word of caution on this: don't give every group of enemies someone with spells that can knock them out of the sky. Don't even give most of your groups that ability. Doing so will essentially be ruining the player's fun. It would be on a similar level to constantly taking the Wizard's spellbook. If they can do a cool thing, let them do the cool thing, but don't let them do it freely and without consequence. It will only take one or two instances of your Aarokocra plummeting out of the sky, magically fast asleep or restrained by vines, before they rethink whether they want to fly that high.
Occasionally have flying enemies
Aarakocra players who spend every fight hovering just out of range tend to feel that they're safe just because they're in the sky. It's your job to disabuse them of this notion. Occasionally have the player encounter an enemy with a fly speed that would be a good challenge for the whole group, and have the enemy go after the flying player.
At this point, your player will realize that what they've done is to isolate themselves far from the rest of their party, out of range of most spells and in a location the rest of the party can't reach. A territorial griffon wouldn't be very hard for a low-level party to handle, but could be absolutely terrifying for a lone Aarokocra. That could turn into a very interesting fight as they desperately try to descend to their party's reach while being grappled by the Griffon and provoking opportunity attacks.