The first element is the plural genitive case of kleppr which means "rocky hill".

[11] The coat of arms was granted on 8 July 1983 and it was in use until 1 January 2020 when the municipality was dissolved.

The official blazon is "Argent, flaunches azure" (Norwegian: I sølv to buede blå flanker).

The arms symbolize the Trangfossen waterfall in the Nidelva river, which is now the deepest canyon in Norway measuring 56 metres (184 ft).

The river has been of great importance for the local development, for agriculture and hydroelectricity generation, hence the use of the waterfall as a typical symbol for the municipality.

The mountain Vassfjellet was located along the western border with Melhus Municipality.

The highest point in the municipality was the 816.7-metre (2,679 ft) tall mountain Kråkfjellet.

The municipal council (Kommunestyre) of Klæbu is made up of 23 representatives that are elected to four year terms.