I have had a climbing hydrangea on an east facing wall in my backyard for several years. It bloomed a few years ago but has not since. I have had the trees trimmed around it to allow more light, have added compost and mulch and also have an irrigation system. I have not pruned it as I know the best time to do so is after it blooms. I hesitate to fertilize it as I do not want to encourage more green growth. Do you have any suggestions of what else I can do to get blossoms?
Judging by your photo, it looks like the hydrangea is getting sufficient light. I have 2 and can testify that, given time, they will bloom even on a dark north facing fence. They are considered to be a good plant to grow in part to full shade.
A flowering plant that is growing well with lots of leaves and sited in an appropriate location but not flowering may not be getting the right nutrition. Often too much nitrogen will promote good leafing at the expense of flowering. Possibly your compost is high in nitrogen. Try fertilizing the hydrangea with a fertilizer that has more potassium than nitrogen (the center number on the fertilizer container ie 5-10-5 ). Sometimes the excess nitrogen comes from fertilizing a nearly lawn.
Flowers also form best on the horizontal branches. Training some of the branches to lie horizontally may help to promote flowering. Also keep in mind that this is a slow growing plant and may take a while to finally bloom. Both of mine took a few years but now bloom well so be patient with it as it is a lovely plant.
Take a look at this link on our web site to another question about climbing hydrangeas that gives some additional growing information:
https://www.torontomastergardeners.ca/askagardener/climbing-hydrangea/