What do you mean by private? Is it a secret registration? Also without knowing the year and make of your car it is difficult to estimate how much it is worth.
...... and I think that the question-asker means 'personalised' registration plate.
The answer is 'as much as someone is willing to pay for it'.
One can get a rough idea of asking prices for similar places by scanning the many trade sources of such plates for sale. Then maybe think about two-thirds of what you read there.
Go to the DVLA personal numbers website and look up a similar registration to see how much they would sell it for.
Other than that it's just waiting around for offers.