As part of adding your girlfriend to the mortgage, the lender will ask if she is named on any existing mortgages and this will need to be declared. A mortgage is a joint and several (individual) contract so your girlfriend is liable for the whole of the existing mortgage debt until she is released from her covenants and for her to be also named on your mortgage she would have to earn enough to cover the whole of both debts.
It is possible but I think very unlikely, that your existing lender would accept a guarantor for her and allow your ex wife to be released. The only way to find out for sure is to ask them and I expect that you would not get an answer until you submitted an application.
You will need to speak to a solicitor and they can advise you whether or not there is any action you can take to get your girlfriend’s name off her existing mortgage.
