Possible Clues:

• Removing dirt
• Washing, dusting
• Wiping the glasses, for example, for neat gin cocktail
• Freeing from dirt
• Stick around college official losing the head working with the Polish
• Conservative propensity for sponging, perhaps?
• Making a big profit, with 'up'
• Routine dental visit
• The century is inclined to the wash
• Cling around an E