Where could I move this to?

This plant has been in the pot for well over 5 years, maybe closer to 10.
I can't remember the name of it so ID would be useful.
I want to repot it into a larger, nicer container
It is in a sheltered position and gets a bit of sun from east and west . It can stay where it is but I wondered where else I could put it

 

The plant in the image appears to be a variety of dwarf conifer, most likely a Cryptomeria japonica (Japanese Cedar) such as the 'Vilmoriniana' cultivar.

• Type: Dwarf evergreen conifer.
• Appearance: Dense, dome-shaped or spherical habit with needle-like green foliage.
• Usage: Popular in rock gardens, containers, and small landscapes due to its compact size and slow growth.
• Seasonal Change: Foliage may turn a bronzy-brown color during autumn and winter.

 

Thank you @Logan. I googled it but the leaves aren't right and the name is unfamiliar.
The foliage is soft and it does sometimes go a bit red. It looks a bit domed as I gathered it up together a few years ago and it gave in to the extent that I could remove the bit of string -eventually.
Ps I seem to remember the Latin name involves the letter T. However, I can't guarantee the it's even at the beginning of the name

 

@Silver surfer might well be able to help .
My guess would be Yew (Taxus) going by what you have said.