#Assuming a willing target, you could do this

After you cast Haste, targeting the enemy, you can release concentration on the opponent's turn.

You can end concentration at any time (no action required).

A willing creature, as defined in this answer, is one who consents to the casting of a spell. Whether a creature would be consenting to a hostile creature casting haste on it depends on it's ability to identify the spell, it's knowledge of it's effects, and it's relationship and faith in the caster. All of these things are under your DM's control, so only your DM can know if a creature would be willing to be targeted by the spell.

After it has consented to the spell, however, it seems unlikely that you would perform any action between the casting of the spell and its turn to make it suddenly unwilling, so the spell would be likely to be active until you choose to release it.

Assuming a willing target, you could do this

After you cast Haste, targeting the enemy, you can release concentration on the opponent's turn.

You can end concentration at any time (no action required).

A willing creature, as defined in this answer, is one who consents to the casting of a spell. Whether a creature would be consenting to a hostile creature casting haste on it depends on it's ability to identify the spell, it's knowledge of it's effects, and it's relationship and faith in the caster. All of these things are under your DM's control, so only your DM can know if a creature would be willing to be targeted by the spell.

After it has consented to the spell, however, it seems unlikely that you would perform any action between the casting of the spell and its turn to make it suddenly unwilling, so the spell would be likely to be active until you choose to release it.

#Assuming a willing target, you could do this

After you cast Haste, targeting the enemy, you can release concentration on the opponent's turn.

You can end concentration at any time (no action required).

A willing creature, as defined in this answer, is one who consents to the casting of a spell. Whether a creature would be consenting to a hostile creature casting haste on it depends on it's ability to identify the spell, it's knowledge of it's effects, and it's relationship and faith in the caster. All of these things are under your DM's control, so only your DM can know if a creature would be willing to be targeted by the spell.

After it has consented to the spell, however, it seems unlikely that you would perform any action between the casting of the spell and its turn to make it suddenly unwilling, so the spell would be likely to be active until you choose to release it.

#Assuming a willing target, you could do this

After you cast Haste, targeting the enemy, you can release concentration on the opponent's turn.

You can end concentration at any time (no action required).

A willing creature, as defined in this answer, is one who consents to the casting of a spell. Whether a creature would be consenting to a hostile creature casting haste on it depends on it's ability to identify the spell, it's knowledge of it's effects, and it's relationship and faith in the caster. All of these things are under your DM's control, so only your DM can know if a creature would be willing to be targeted by the spell.

After it has consented to the spell, however, it seems unlikely that you would perform any action between the casting of the spell and its turn to make it suddenly unwilling, so the spell would be likely to be active until you choose to release it.

#Assuming a willing target, this would take two of your own actions.

With the first action, you'd cast Haste, targeting the enemy. The second action would then be used to Ready an action, with which you'd release concentration on the opponent's turn. You'd have to come up with some perceivable trigger, but that would be the only way to end concentration on the enemy's turn without being attacked.

The risk of this method is that without Action Surge from two levels of fighter, you'd be unable to do this in a single round, meaning the enemy would reap at least one round's benefit from the haste spell.

I assume a willing target with all of this, because I unfortunately cannot say whether there's a way to make a target willing.

#Assuming a willing target, you could do this

After you cast Haste, targeting the enemy, you can release concentration on the opponent's turn.

You can end concentration at any time (no action required).

A willing creature, as defined in this answer, is one who consents to the casting of a spell. Whether a creature would be consenting to a hostile creature casting haste on it depends on it's ability to identify the spell, it's knowledge of it's effects, and it's relationship and faith in the caster. All of these things are under your DM's control, so only your DM can know if a creature would be willing to be targeted by the spell.

After it has consented to the spell, however, it seems unlikely that you would perform any action between the casting of the spell and its turn to make it suddenly unwilling, so the spell would be likely to be active until you choose to release it.