American President’s terribly mediocre (10)
I believe the answer is:
pedestrian
'mediocre' is the definition.
(thesaurus)
'american president's terribly' is the wordplay.
'american' becomes 'a' (common abbreviation - e.g. in organisation names).
'terribly' indicates an anagram.
'a'+'president'='apresident'
'apresident' is an anagram of 'PEDESTRIAN'.
(Other definitions for pedestrian that I've seen before include "One walks around" , "lame" , "not very fast" , "footman" , "A person travelling on foot" .)