Having started his career as a repertory actor and film extra, Conrad was cast in a television play Bye, Bye Barney as a pop singer. He was noticed by Jack Good who included him in his TV series Oh Boy!, and then was signed to Decca Records and had a number of chart hits, including "Cherry Pie", "This Pullover", "Mystery Girl" and "Pretty Jenny"; also recording for Columbia, Pye President and EMI.
Between the late 1950s and mid-1960s, Conrad appeared in a number of films such as Serious Charge (uncredited), The Boys, Rag Doll, (filmed in 1960, and released in 1961); K.I.L. 1 and Konga as well as Michael Powell's The Queen's Guards. Conrad played Danny Pace in an episode of The Human Jungle called "The Flip Side Man" in 1963.
During the 1970s, he spent some time in the stage shows Godspell and Joseph and the Amazing Technicolor Dreamcoat, and also featured in a cameo role in the Sex Pistols film The Great Rock 'n' Roll Swindle. In 1977 no fewer than seven of Conrad's singles were included in the 'World's Worst Record' list, chosen by listeners to Capital FM DJ Kenny Everett's show, and "This Pullover", voted sixth worst song ever, later featured on The World's Worst Record Show, a 1978 LP dedicated to the songs voted for, together with two other Conrad recordings "Cherry Pie" and "Why Am I Living?" He also made an appearance in Are You Being Served as Mr Walpole, head of sporting equipment, in the episode "Memories Are Made Of This".
In the 1990s, Conrad made regular cameo appearances on Jim Davidson's revived version of The Generation Game on BBC1. Also in 1992 Conrad appeared in the Christmas Special of Big Break, also presented by Davidson and John Virgo. He was the "booby" prize of the show presented to Hi-de-Hi! actress Ruth Madoc. Contestants who failed to make the final of Big Break were often nearly given a box set of Conrad's hit singles.
Since then, Conrad has appeared in a number of documentaries and television programmes, often offering stories of violent encounters with other famous people. In a BBC Arena documentary about the record producer Joe Meek, Conrad boasted of biting off part of the nose of the singer Heinz during a confrontation backstage at a package show in the early 1960s. Similarly, in Sex, Secrets & Frankie Howerd, he told of threatening to cut off comedian Frankie Howerd's ears when Howerd made undesired sexual advances to him in a dressing room.
In the 2009 film Telstar: The Joe Meek Story, Conrad is played by Nigel Harman. Conrad himself appears in one scene, depicting his backstage fight with Heinz and his biting of Heinz's nose. Conrad also plays the role of Larry Parnes in the film.
Conrad is a member of the show business fraternity the Grand Order of Water Rats, having served as "King Rat". He is also a Freemason and a member of Chelsea Lodge No. 3098, the membership of which is made up of entertainers. He was appointed an Officer of the Order of the British Empire (OBE) in the 2011 Queen's Birthday Honours for charitable services. In 2018, he appeared in ITV's Last Laugh in Vegas.
- "Cherry Pie" / "There's Gonna Be A Day" 1960
- "Out Of Luck" / "Unless You Mean It" Decca UK 1960
- "Mystery Girl" A2: Just The Two Of Us B1: (I Wanna) Love My Life Away B2: Maybe You'll Be There 1961 EP
- "Mystery Girl" / "The Big White House" 1961
- "This Pullover" / "Why Am I Living" 1961
- "I See You" / "Oh! You Beautiful Doll" 1961
- "Every Breath I Take" / "Walk Away" 1961
- "Twist My Wrist" / "Hey Little Girl" 1961
- The Cockleshell Heroes (1955) – Sailor in Pub (uncredited)
- Wicked as They Come (1956) – Dancer in Club (uncredited)
- My Teenage Daughter (1956) – Dancer (uncredited)
- Further Up the Creek (1958) – Signalman (uncredited)
- Serious Charge (1959) – Dancer (uncredited)
- The Ugly Duckling (1959) – Bimbo
- Friends and Neighbours (1959) – Buddy Fisher
- Follow a Star (1959) – Theatre Heckler No. 3 (uncredited)
- Too Young to Love (1960) – Peter Martin
- Rag Doll (1961) – Shane
- Konga (1961) – Bob Kenton
- The Queen's Guards (1961) – Dankworth
- K.I.L. 1 (1962) – Ted-o
- The Boys (1962) – Barney Lee
- Aliki My Love (1963) – Barry Wilson
- The Golden Head (1964) – Michael Stevenson
- The Amorous Adventures of Moll Flanders (1965) – First Mohock
- Hell Is Empty (1967) – Jess Shepherd
- The Assassination Bureau (1969) – Angelo
- Cool It Carol! (1970) – Jonathan
- The Flesh and Blood Show (1972) – Young Actor
- The Great Rock 'n' Roll Swindle (1980) – Jess
- The Body in the Library (film) (1984) – Raymond Starr
- Claudia (1985) – Man at Deli
- Absolute Beginners (1986) – Cappuccino Man
- Tank Malling (1989) – Celebrity
- The Punk and the Princess (1993) – Rachel's Father
- Telstar: The Joe Meek Story (2008) – Larry Parnes
- Zero (2011) – Lottery Presenter
- Run for Your Wife (2012)
- Mob Handed (2016) – The Judge
- "Looking Back With Jess" (PDF). Jessconrad.com. Retrieved 18 April 2017.
- Colin Larkin (1997). Virgin Encyclopedia of Sixties Music. Muze UK Ltd. p. 125. ISBN 0-7535-0149-X.
- Colin Larkin, ed. (1997). The Virgin Encyclopedia of Popular Music (Concise ed.). Virgin Books. p. 297. ISBN 1-85227-745-9.
- Bill Bailey. "Kenny Everett's World's Worst Wireless Show, Kenny Everett, World's Worst Records, Worlds Worst Records". Chronoglide.com. Retrieved 18 April 2017.
- "Archived copy". Archived from the original on 22 July 2011. Retrieved 12 October 2009.CS1 maint: archived copy as title (link)
- "The Strange Story of Joe Meek". IMDb. Retrieved 12 March 2011.
- "BBC: Jess Conrad bites off fellow singer Heinz's nose". BBC. Retrieved 20 March 2011.
- "All Water Rats". Gowr.co.uk. Retrieved 18 April 2017.
- Ray Donn. "Chelsea Lodge No 3098". Chelsea-lodge.org.uk. Retrieved 18 April 2017.
- "Viewing Page 9 of Issue 59808". London-gazette.co.uk. 11 June 2011. Retrieved 31 December 2011.
- "Jess Conrad BIOGRAPHY". Jessconrad.com. Retrieved 14 October 2019.