^^^ That's one of those 'How long is a piece of string' questions, Conne!
If a solicitor is involved, and the estate is complex, then it can take over a year (or even, in very rare cases, several years).
However if the estate is fairly straightforward, with the executors doing all of the work themselves (and 'really getting on with it'), then it can be quite a quick process (in relation to how long other legal matters can often take).
My father died in mid-October. I'd sought and obtained probate, and was driving a car bought from the money in his estate, by the end of November.
So there's a very wide range of possible answers to your question but 'a few months' might be typical where an estate is uncomplicated.