Rest arrive briefly for TV programme (6)
I believe the answer is:
sitcom
'tv programme' is the definition.
(type of TV programme)
'rest arrive briefly' is the wordplay.
'rest' becomes 'sit' (I've seen this in another clue).
'arrive' becomes 'come' (synonyms).
'briefly' means to remove the last letter.
'come' with its last letter removed is 'com'.
'sit'+'com'='SITCOM'
'for' is the link.
(Other definitions for sitcom that I've seen before include "Humorous situation drama, in short" , "Friends, for example" , "Form of TV comedy" , "Kind of TV programme" , "Light-hearted TV series" .)