Mildred Fletcher was a nurse that appeared in Series 8. She was the head nurse of the Psychiatric Hospital in which Frank Gallagher was being held. Frank was being held under the pretense that all the details of his real life were a delusion, Nurse Mildred was the main person behind this because she was in a relationship with Monica Gallagher.
Monica convinced Mildred to hold Frank so that she could challenge their divorce and ruin his upcoming wedding to Libby Croker.
Monica mentioned at the beginning of Series 8 that she had married another woman in a civil partnership, it can be assumed that the woman she married was Mildred.