Mark has a fresh hope — to restrict bad temper (10)
I believe the answer is:
apostrophe
'mark' is the definition.
(punctuation mark)
'a fresh hope to restrict bad temper' is the wordplay.
'fresh' indicates an anagram.
'to restrict' indicates putting letters inside.
'bad temper' becomes 'strop' (strop can mean a temper tantrum).
'hope' with letters rearranged gives 'pohe'.
'pohe' enclosing 'strop' is 'postrophe'.
'a'+'postrophe'='APOSTROPHE'
'has' acts as a link.
(Other definitions for apostrophe that I've seen before include "Often misplaced punctuation mark" , "Part of man's" , "detail of punctuation" , "Single quote mark" , "in Charley's Aunt ?" .)