I am a carer, can I use my client's ATM card on their behalf?

If you work for an agency, check with them to find out their policy on this. You don't want to lose your job if it is against policy however much you want to help. If you are not with an agency or they have no policy against it, have the individual write and sign a dated note with the specific amount she wants withdrawn, get a receipt when you do the withdrawal, and attach the receipt to the note so if there is any question in the future, you have a record of permission for each withdrawal.