[5] In 2014, he was appointed as interim chair of the Department of Surgery at University Hospitals Case Medical Center and interim surgeon-in-chief of the University Hospitals Health System, while maintaining his role as chief of the division of colorectal surgery and surgical director of the UH Digestive Health Institute.

[12] Delaney was listed as a possible successor to Dr. Toby Cosgrove as the CEO of the Cleveland Clinic while the Chairman of the Digestive Disease and Surgery Institute in 2017.

[28] Delaney's clinical contributions include work in minimally invasive laparoscopic colorectal surgery to enhance recovery,[29][30] of which he has demonstrated associated short and long-term cost-savings.

[48][49][50] Using routinely captured data, the HARM Score decreased administrative costs associated with quality care improvement programs, while being almost universally applicable regardless of the size of the hospital.

[56][57] He created the venture while Chief of the Division of Colorectal Surgery at UH Case Medical Center, seeking to find what factors truly drove cost in the operating room and were associated with readmissions within 30 days of discharge.

[58] Delaney was quoted saying, "Socrates gives hospitals the opportunity to interpret complex administrative data and view trends, outliers and variability in the process, so they can improve their efficiency and terms of care.

[27][67][68] In September 2018, Delaney was invited to deliver the keynote address at the 43rd Sir Peter Freyer Memorial Lecture and Surgical Symposium in Galway, Ireland.

[71][72][73][74] In the acknowledgement for his book, Delaney credits his father, Peter, "whose love of surgery and its ability to help others led [Conor] to this field.

"[75] Delaney's maternal great-grandfather was Edward Peter O'Kelly, who served two terms as a Member of the British House of Commons.