Hi Astri. I am in Canberra and have nineteen trees in our garden. How big is your block? Which way does it face for solar access? Do you have any power lines or easements to consider? What plans do you have for dealing with the autumn leaves? I'm not quite sure what you mean by a gatehouse and arbour on the fenceline but have you checked the regulations for structures on your boundary? Where do you want to plant the hedge and what is the width?

looks like one of the Philodendrons or similar plants that are usually grown in pots as indoor plants but anything growing in brickwork needs to be removed to avoid damage to the wall

I'd normally say go for a row of ornamental pears but I think it might look funny given your row of connifers as you don't want to look boxed in. I'd think about disguising neighbours with a single largish specimen tree in that side with lots of underplanting. You can't realistically block out all unattractive parts of outside your yard and what you really want to do is create interest in the foreground so it draws the eye in. Or else do the row of pears but create a bed in front of connifers and plant variety there (bearing in mind how connifers change soil acidity).

The tree would be to replace the silver birch in the photo which doesn't provide much shade.