How long does a palm tree take to grow leaves?

It is possible, and it isn't possible. It would be nice to know exactly what tree it is that you are talking about, but there is a 99% chance that it will lose its leaves. Some trees never lose their leaves, though.

No, not all trees lose their leaves. Some trees their leaves all year round. They are called evergreens because they are always, or forever, green. They include spruces and pines, as well as cedars and firs.

View the related link below for more information on evergreen trees.