Mulberry

If it is getting to be rootbound, then you need a bigger pot - but don't go too much bigger as you don't want the roots to be swimming around in lots of spare compost. 

The general approach would be to use a John Innes number 3 type compost.  This is a particular formula (made by various manufacturers) which contains a higher proportion of soil than the lower John Innes numbered composts.  Therefore the nutrients and water retention are better, because this is a permanent planting rather than an annual crop.

Try to plant at the same compost level as the current plant, and add some fertiliser into the planting hole - hopefully others will confirm whether a general purpose fertiliser like fish blood and bone, or growmore, would be best - or whether something more bespoke / single fertiliser would be preferable (I'm rubbish on fertilisers).

No idea about where to get the pot, sorry.