Is Ivy Harmful to Trees ?

The not so simple answer is yes and no.

In most cases the ivy will not harm a tree and will only cause a problem if it has been growing for so long that its weight and spread cause damage. We had a large ash tree that had ivy up it but the ash tree was over 40ft high with a trunk diameter of nearly 6ft. The ivy had a trunk with a diameter of 6".

One of the causes of ivy growing up trees at a rate that bothers them is when the tree is not doing very well. The ivy, naturally, climbs the tree for the light. Trees that are not doing very well tend to have their crowns quite open and not enough leaf. This gives extra light and encourages the ivy to climb.

If it's a small tree then I would be inclined to just remove the ivy - unless it's an ornamental one.

A picture, or two, would be of help.

Re ash trees:- they can be a nuisance. They tend to grow fairly quickly and can outgrow small gardens. Also, the seeds (keys) can grow in the ground very easily. Make sure that you keep a good eye out for young ones growing and remove them as soon as possible. They have a taproot that goes down very quickly and even something only a couple of years old can be difficult to get out.