The grappling rules state:

Moving a Grappled Creature.

When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.

If I have 30 speed and have an enemy grappled, then I move 15 feet and release my grapple on my target, do I still have 15 feet of movement left, or is it lost for the round?

It's the same as moving through difficult terrain

You can release the target at any time, effectively changing your speed:

you can release the target whenever you like (no action required)

You will get your normal speed, but you won't get your movement back. In 5e "speed" is not equal "movement". For example, if your walking speed is 30ft, you can move up to 30 feet per turn; when you moved 30 feet, your speed is still 30, but now you have 0 movement.

After you moved 15 feet with 15ft speed you have 0 movement left. Even if you get faster speed afterwards, it won't give you any extra movement (otherwise, you could move your normal 30 feet this round, regardless of the fact that your speed was halved).

@Slagmoth added a fair point here:

I honestly think the devs used a poor word choice on this. It would be easier to think about it the same way as difficult terrain which would be that it costs you twice as much to move a given distance as opposed to halving your speed.

It seems Mike Mearls (whose rulings are not official) uses the same ruling:

Things like caltrop/ball bearings ref to moving at half speed how do you do that? Treating each 5' as 10 like difficult terain?

yes, essentially pay an extra 1' per 1' moved

After releasing the grapple, you can move 15 more feet

Movement speed is only halved while you are dragging the creature

When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.

The condition is clear, when you move with a grappled creature your speed is halved. If you are no longer moving with a grappled creature, this rule no longer applies and your speed becomes normal.

When your speed changes, the amount you can move also changes

On your turn, you can move a distance up to your speed.

This is a simple rule and it has no qualifiers. During one round you can move up to whatever your current speed is. It doesn't mention any exceptions for cases where your speed might increase or decrease during the turn. So if your speed increases during your turn, you can move further that round. If it decreases, so does the distance you can move.

Thus, if you move 15 feet with your grappled creature you have moved 15 feet with a speed of 15. After releasing the grapple, your speed becomes 30. And, according to the rules, you can move a distance up to your speed on your turn. Since you have already moved 15 and you have a speed of 30, you have 15 feet more you can go.

No. When you move with a grappled creature your speed is halved.

tl;dr As soon a character moves with a grappled creature, your speed is halved. Releasing the creature does not undo the halved movement for the round.

Moving a Grappled Creature. When you move, you can drag or carry the grappled creature with you, but your speed is halved, unless the creature is two or more sizes smaller than you.

E.g.

1. A character with move speed 30 begins to drag a grappled creature.


2. The move speed is now halved to 15.


3. The character moves 5 feet and releases the creature.


4. The character has 10 feet of move remaining.

Specifically answering the above situation: The character begins to drag a grappled creature. Their speed is halved to 15. They move 15 feet. They release the creature. They have 0 movement remaining. Dragging the creature halved their movement.

Grapple is not using different move speeds.

If grapple were a separate move speed, then a character could use both in the way the question describes.

Using Different Speeds

If you have more than one speed, such as your walking speed and a flying speed, you can switch back and forth between your speeds during your move. ...

For example, if you have a speed of 30 and a flying speed of 60 because a wizard cast the fly spell on you, you could fly 20 feet, then walk 10 feet, and then leap into the air to fly 30 feet more.

Look at Speed and movement like a glass of water. Each turn you start with a full glass. Usually you have 30 oz of water in your glass to spend however you'd like. While grappled, it takes 10oz of water to move 5ft. If you've spent 3 sets of 10 oz to go 15ft, your glass of water is empty, no matter how fast you can move after that.

If for instance you move 5ft while grappled, you spend 10oz of water. You still have 20oz left. If you moved another 5ft, that's another 10oz. If you let go of your grapple now, your speed effectively goes back up to normal and you can spend the last remaining 10oz of water in your cup to move 10ft.

Hope this analogy helps visualize the difference between capacity and usage.