A graduate of Lincoln High School, Dave Klemm was a two-time state qualifier for Hall of Fame coach Floyd Bee, placing third as a senior. During his senior summer he won the AAU Junior Nationals tournament and the USA Junior Nationals tournament.

Klemm's collegiate career took place at Eastern Illinois University. While at Eastern, he was a four-time NCAA All-American placing third, second and first in NCAA Division II and second in NCAA Division I.

In 1979, Klemm was a member of the USA World Team and competed in the World Championships. In 1980 due to the Olympic boycott, Klemm turning his sights to coaching.

Klemm's coaching career began in 1980 as an assistant at Eastern Illinois. In 1982, after two years as the EIU assistant, Klemm headed to the University of Oklahoma as an assistant from 1982-84. In 1984, Klemm returned to the state of Illinois where he was an assistant coach at the University of Illinois from 1984-87. In 1987, Klemm returned to Eastern Illinois as an assistant coach from 1987-89. During this time, Dave earned a bachelor's degree in sports administration.

Klemm's head coaching career began in 1989 when he became the wrestling coach and physical education instructor at MacMurray College. In 1991, Klemm became the head wrestling coach and physical education instructor at Lincoln College. While coaching at Lincoln, Klemm produced 174 Junior College national qualifiers, 58 All-Americans, and nine national champions. His teams finished in the top six eight times. Klemm was voted National Junior College Athletic Association Region Coach of the Year three times, National Coach of the Year in 1997, and Man of the Year in 1999.

Klemm was inducted into the Eastern Illinois University Athletic Hall of Fame in 1989, the Illinois Wrestling Coaches and Officials Association Hall of Fame in 1996, and the NJCAA Hall of Fame in 2003. He received the Lifetime Service to Wrestling award from the Illinois Chapter of the National Wrestling Hall of Fame in 2013 and the Lifetime Achievement award from the IWCOA in 2015.

From 1991 to 2008, Klemm was a tenured faculty member at Lincoln College in physical education. In addition to his duties, Klemm was named physical education division chair in 1999.

In 2008, Klemm left the classroom for an administrative position, being named director of athletics, in addition to coaching wrestling. In 2011, Dave stepped down as head wrestling coach allowing more time to concentrate on administrative duties.

Under his administrative direction, Lincoln College athletic teams produced 14 individual national champions, 17 national-placing teams and two national champion teams. In 2014, after the departure of the wrestling coach, Klemm stepped back into the head coach position for two years.

In 2016, Klemm stepped away from wrestling for good and focused on the transition process of Lincoln College to a four-year athletic program. In 2017, Klemm chaired a committee that complied inform and submitted the application for acceptance to the National Association of Intercollegiate Athletics (NAIA).

Dave retired from Lincoln College in December of 2017. Dave and his wife Linda live in Warrensburg, Illinois with their two children, Sara and Evan.