After beginning his career at club level with Bennettsbridge, Cleere joined the Kilkenny minor team as a 17-year-old in 1958 and subsequently had a brief stint with the junior side.
From his debut, Cleere was ever-present as a right wing-back and made 22 championship appearances in a career that ended with his last game in 1969.
His club career yielded six Kilkenny County Championship titles during a golden age for Bennettsbridge.
After coming to prominence at juvenile and underage levels, he became a starting fifteen regular with the club's senior team during the 1959 Kilkenny County Championship.
Cleere ended his first full season at senior level with a Kilkenny County Championship medal after a 4-06 to 1-04 win over Erin's Own in the final.
Bennettsbridge again failed to retain the title, however, Cleere added a fourth winners' medal to his collection after a 4-09 to 1-04 defeat of Glenmore in the 1964 final.
He won a Leinster Minor Championship medal as an unused substitute when Kilkenny beat Laois by 5-11 to 1-07 in the final.
He made his debut at right wing-back, with his brother Liam lining out in goal, on 3 April 1960 in a 4-07 to 2-07 win over Wexford.
Described in the Irish Independent as having a "superb game", he claimed his first All-Ireland medal and had the honour of lifting the Liam MacCarthy Cup after the 4-17 to 6-08 victory.
[5][6] In spite of this defeat, Cleere ended the season with a second National League winners' medal after an aggregate victory of 10-15 to 2-15 over New York in the final.
He subsequently claimed his eighth provincial winners' medal as a non-playing substitute after the 3-09 to 0-16 defeat of Offaly in the final.