Known to Worcestershire folk as "Apple Norm", Gifford served his apprenticeship as a professional cricketer in the Worcestershire second team during 1959, and when in May 1960 he took 2–25 from 18 overs in a drawn Second XI match against Kent, he was called up to the first team for the game against the same opposition that began the very next day. Gifford took four wickets in Kent's first innings, but Worcestershire collapsed to their second-lowest ever score of 25 all out on their way to an innings defeat. In the next game against Cambridge University Gifford took ten wickets in the match, including second-innings analysis of 15.5–7–18–6.

Gifford finished 1960 with 41 wickets at an average of 17.90, but this only hinted at the success he was to enjoy the following year. 1961 proved to be the most productive season of Gifford's career as he took 133 wickets. In July 1961, he was notified he was on the long list to tour India and Pakistan with the Marylebone Cricket Club (MCC) side, but was not selected for the final party. In compensation he toured Rhodesia and Pakistan with an International XI. He was again fairly successful in the 1962 and 1963 seasons, with 92 and 72 wickets respectively, and in 1962 was selected for the Players in their final match against the Gentlemen before the distinction between amateur and professional cricketers was abolished.

1964 was the year when Gifford really broke through as he was selected for the Second Ashes Test at Lord's in June. Although the game was ruined by rain, with no play at all possible on the first two days, Gifford had time to impress, returning miserly analyses of 12–6–14–2 in the first innings and 17–9–17–1 in the second. He was retained for the Third Test at Headingley, but took only two wickets as Australia recorded a comfortable win. It would be seven years before he played Test cricket again.

Worcestershire's won the County Championship in 1964, and retained their title the following year. Gifford was instrumental in these successes, and although he reached 100 wickets only in 1964, between 1963 and 1968 he averaged under 20 with the ball every season. He took his career-best bowling figures in July 1968 when he took 8–28 (albeit in a losing cause) against Yorkshire.

Gifford was recalled to the England team in 1971, replacing Derek Underwood for the Second Test against Pakistan. He was in and out of the team during the next two years, including a tour of the Indian sub-continent in 1973-4.

He played two more Tests against New Zealand the following summer, but thereafter the select