The aim of this work is the dosimetric characterization of a plane parallel ionization chamber under defined beam setups at the CERN Linear Electron Accelerator for Research (CLEAR). A laser driven electron beam with energy of 200 MeV at two different field sizes of approximately 3.5 mm FWHM and approximately 7 mm FWHM were used at different pulse structures. Thereby the dose-per-pulse range varied between approximately 0.2 and 12 Gy per pulse. This range represents approximately conventional dose rate range beam conditions up to ultra-high dose rate (UHDR) beam conditions. The experiment was based on a water phantom which was integrated into the horizontal beamline and radiochromic films and an Advanced Markus ionization chamber was positioned in the water phantom. In addition, the experimental setup were modelled in the Monte Carlo simulation environment FLUKA. In a first step the radiochromic film measurements were used to verify the beamline setup. Depth dose distributions and dose profiles measured by radiochromic film were compared with Monte Carlo simulations to verify the experimental conditions. Second, the radiochromic films were used for reference dosimetry to characterize the ionization chamber. In particular, polarity effects and the ion collection efficiency of the ionization chamber were investigated for both field sizes and the complete dose rate range. As a result of the study, significant polarity effects and recombination loss of the ionization chamber were shown and characterized. However, the work shows that the behavior of the ionization chamber at the laser driven beam line at the CLEAR facility is comparable to classical high dose-per-pulse electron beams. This allows the use of ionization chambers on the CLEAR system and thus enables active dose measurement during the experiment. Compared to passive dose measurement with film, this is an important step forward in the experimental equipment of the facility.