It is perfectly legal to live with someone before your divorce happens.

However whether you divorce or not it is a good idea to commence a property settlement with your former partner before you take up a new relationship, the reason is that if this happens after the new relationship starts there may be problems if the new partner brings property into your new relationship and your former partner claims they were assets from the old relationship.

These things can usually be sorted out, but that sorting out could cost you money in legal fees.

You need a new partner???

Keep good records and see if you can ring fence any investments or property. Then any tactics (as MartinO is suggesting) your ex might use to harass your new partner will fail.