Clue: Like the Sphinx, reportedly, if accepted (11)
Answer: WEATHERWORN
Explanation: Definition: Like the Sphinx
 **Homophone of**(reportedly) "whether"("if", as in "I couldn't tell whether he was right or wrong") + WORN(past tense of "wear", informal term for "accept"/"tolerate", as in "I wanted to try a new approach, but my boss wouldn't wear it").
: Note the weatherworn face.