Gross wig he sported in public (10)
I believe the answer is:
overweight
'gross' is the definition.
(thesaurus)
'wig he sported in public' is the wordplay.
'sported' indicates an anagram (I've seen 'sport' mean this).
'in' indicates putting letters inside.
'public' becomes 'overt' (both can mean well-known or unconcealed).
'wig'+'he'='wighe'
'wighe' is an anagram of 'weigh'.
'weigh' going within 'overt' is 'OVERWEIGHT'.
(Other definitions for overweight that I've seen before include "Carrying a lot of stones" , "stout" , "Big" , "Too heavy" , "Obese" .)