The Baron was the grandson of Sir Charles Tennant, 1st bt., well-known art collector, patron, and museum trustee. Christopher Tennant inherited many paintings and other works of art from his grandfather. He succeeded his father, Edward Priaulx Tennant, 1st baron Glenconner, as baron in 1920. He was the Chairman of Northern Assurance Co. Ltd., and of C. Tennant, Sons and Co. Ltd.; he also directed the Hambros Bank Ltd. In 1925 he married Pamela Winifred Paget (1903-1989), daughter of Sir Richard Paget, 2nd bt. They had two sons, and were divorced in 1935. He was married a second time to Elizabeth Powell, and with her had a son and two daughters.