Clue: Rude character that is not apparent in Michael Caine's performance (10)
Answer: MECHANICAL
Explanation: Definition: Rude character
 **Anagram of**(…'s performance) [ "Michael Caine" **minus**(… not apparent) "i.e."(abbrev. for "id est"/that is) ].
Defn: In Shakespeare's "A Midsummer Night's Dream", one of the 6 amateur actors called "rude mechanicals" by Puck, in reference to their occupations as manual labourers.