I would like to add a Live Tile to display the current time (only minutes accuracy).
Is there a tile for the builtin clock? Is there an app?
Developers may only update Live Tiles every half hour. Being an OEM partner HTC is the only one being able to offer a clock where the tile can update every Minute. But as Maura said, this is currently exclusive to the 8X (and 8S I guess).
Note: For Windows Phone 8
There are multiple clock apps, both analog and digital, if you check the store. A good (free) one is called "World Clock" from Live Apps - you can create one or more live tile clocks.
The HTC 8x has an in-the-box time tile, by the way but it's currently unique to the 8x.