Given the tendency for C Montana to be a strong growing plant, I wouldn't advise it. Depends on how old/well established your Apple is and how much clear ground you have around the base as to whether you could choose a less aggressive climber ? Planted close together, there will be competition for water and nutrients. You have more options if you just wish to use the Apple tree as a support rather than making use of any fruit.
I had a Clematis rehderiana growing through quite a beast of a Bramley apple tree. It just becomes a tangle and quite unsightly except for a few months. When it's not unsightly it affects the health of the tree by introducing congestion and reducing air circulation - I took it out.
And think of the weight of all that Clematis. It would end up pushing the apple boughs downward. In winter it would look like Arthur Scargill’s barnet.
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Depends on how old/well established your Apple is and how much clear ground you have around the base as to whether you could choose a less aggressive climber ?
Planted close together, there will be competition for water and nutrients.
You have more options if you just wish to use the Apple tree as a support rather than making use of any fruit.
I wouldn’t do it to a healthy productive tree.