Sioux
If your ESA is wholely Income Related ESA then this will not be payable if your partner claims Universal Credit, however, your award should be transferred to UC and you will receive the LCWRA element which is the UC equivalent of the SG. You will need to manage this process as it is manual one and may get sidelined in the current situation.
If you are receiving Contribution Based ESA with an Income Related top-up then the ESA(IR) amount will stop, as above, your award will be transferred to UC but your ESA(CB) will be treated as Other Income and deducted from the UC.
If you are only receiving ESA(CB) then it will not be affected, your award will be transferred to UC but your ESA(CB) will be treated as Other Income and deducted from the UC.
Gordon
Nothing on this board constitutes legal advice - always consult a professional about specific problems