TV set remained off for commercial (13)
I believe the answer is:
advertisement
'commercial' is the definition.
(thesaurus)
'tv set remained off' is the wordplay.
'off' is an anagram indicator.
'tv'+'set'+'remained'='tvsetremained'
'tvsetremained' anagrammed gives 'ADVERTISEMENT'.
'for' is the link.
(Other definitions for advertisement that I've seen before include "Bill" , "Commercial promotion" , "Public promotion" , "trailer" , "Placard" .)