What's this small tree and will it stay compact?

I'd keep it, if you like it.
Its not something that has recently been planted, so I'd go with it, if you like it.

But if it should turn out to be Arbutus it's not likely to be very impressed regarding too much lime, so rubble and cement will not do it any good.

 

Are you in the US? I have a viburnum here in the UK, and it looks just like that. It has lovely white flowers in the winter.

 

Typos and spellings aside, I think what you need to learn as a gardener is patience. These things are usually not best decided in an instant or a quick question on an internet forum. Plants progress through the seasons, flowering when they will; you cannot change that. Did it flower last year and have you got a picture? Maybe then you will get an accurate ID. Gardening is about a lot of things, one of the most important being patience.

 

Hello Emma and to GC nice to have you with us

 

UK (I thought this was a UK forum)

 

We moved in within the past year so have no idea what the flowers (if any) look like.

I guess if no-one here knows whether this sort of tree will survive in a brick walled flowerbed (the original question) then it's best to dig it up rather than risk it breaking the wall, or growing into a full tree that may cause subsidence.

 

It is ashirus

 

I've just checked the bark on internet images which suggests it's a Bay tree.

 

The tree in question is without doubt good ol Euonymus japonicus

It won't get much bigger and is easily maintained with judicious pruning.