Turn away, catching start of distasteful commercial (6)
I believe the answer is:
advert
'commercial' is the definition.
(I've seen this before)
'turn away catching start of distasteful' is the wordplay.
'turn away' becomes 'avert' ('avert' can be a synonym of 'turn away').
'catching' means one lot of letters goes inside another.
'start of' suggests taking the first letters.
The first letter of 'distasteful' is 'd'.
'avert' enclosing 'd' is 'ADVERT'.
(Other definitions for advert that I've seen before include "Refer or allude" , "Refer; commercial" , "Promotional notice" , "piece of publicity" , "Notice promoting goods" .)