By the end of the decade, he was a regular in the Palace midfield, and became a fans' favourite by scoring the winning goal in the home tie with Fulham, in 1969, that secured promotion to the First Division for the first time in the club's history. That season, Kember was one of only three players who played in every game.
In the top flight, Steve continued to impress, gaining England U23 caps, and in the summer of 1971, having helped Palace to survival, Steve replaced John Sewell as captain, following his departure to Orient.
However, the captaincy was short-lived, and Kember joined Chelsea for a record fee of £170,000 in September.
At Chelsea, Steve quickly stamped his authority on a place in the starting line-up, playing most of the West-London club's games, that season.
However, Chelsea then fell into decline, and were eventually relegated to the Second Division, at the end of the 1974-75 season. With relegation comes and inevitable sell-off of stars, and Kember moved back to the top-flight, to Leicester City, shortly after Chelsea's relegation.
At first, he was a regular in Leicester's first team line up, but after two seasons, he was little more than a squad player, only appearing in half of Leicester's games in the 1977-78 season.
Early in the 1978-79 season, Terry Venables signed him back to Crystal Palace. While Kember had been away, the south London club's fortunes had taken a dramatic turn for the worst, being relegated to the Second Division in 1974, and again, to the Third, the following year. They had been promoted in the 1976-77 season, but were still a long way behind where they were when Kember left.
Venables' signing of Steve was intended to be as a squad player, but Kember's experience added so much to the side that he quickly became a regular in the first XI. So much so that Palace were promoted back to the First Division, at the end of the season.
He had a largely un-noteworthy couple of seasons in Canada, and in the summer of 1981 he returned to Palace again (who had a new chairman, Ron Noades), this time as a coach for the Youth setup.
He had a relatively successful period, taking the club on an FA Cup run to the Fifth Round, and achieving Second Division survival with a game to spare.
However, for reasons unknown, he was replaced with the highly unpopular Alan Mullery. Kember said of the matter that he was "away on holiday at the time" and thus wasn't even notified of his dismissal.
He then joined non-league Whyteleafe in November 1986, as manager, helping them to the Third Qualifying Round of the FA Cup in the 1988-89 and 1989-90 seasons. In the former, "The Leafe" were also promoted, to the Isthmian League Division One.
In the summer of 1993, Kember resigned (to be replaced by former Palace team-mate Paul Hinshelwood) and once again went back to Palace, as a member of the coaching staff.
He stayed in that role until April 2001, when, with Palace once again looming over relegation to the third tier, manager Alan Smith was sacked by new chairman Simon Jordan, and Kember was made caretaker for the remaining two games.
With two games left in the season, and Palace six points short of survival, it seemed that only a miracle would keep them up.
However, Kember made changes to the side, and after a last-gasp win at Stockport County, Palace survived.
In honour of this achievement, chairman Jordan said that Kember would now have a "job for life," at Palace.
However, this was not the managerial job just yet. Steve Bruce took over, and Kember was made his assistant.
Bruce's tenure only lasted a couple of months, and, after Kember was again made caretaker (this time with Terry Bullivant), Trevor Francis took over. Francis was unpopular with the fans in his 14 months with the club, and was eventually sacked in February 2003, with Kember again being made caretaker, this time alone.
At the end of the season, Kember was made manager full-time, and Palace's 2003-04 season got off to a flying start, the club winning all three of their opening games, to top the table. However, this excellent form soon ended, and by November, Palace were in 20th, and only two points above the drop-zone after losing 5-0 at newly-promoted Wigan Athletic. Jordan saw this as the final straw, and Kember was sacked, clearly revoking Jordan's "job for life" pledge.
However, Kember refuses to hold a grudge against the club, and can be seen at Selhurst Park as a spectator, on occasions.