Starts to read extremely tasteless Conservative homeless gag (5)
I believe the answer is:
retch
'gag' is the definition.
(I know that gag can be written as retch)
'starts to read extremely tasteless conservative homeless' is the wordplay.
'starts to' indicates taking the first letters.
The first letters of 'read extremely tasteless conservative homeless' is 'RETCH'.
(Other definitions for retch that I've seen before include "Heave (as if to vomit)" , "Unsuccessful effort to vomit" , "Reach" , "Gag, near-vomit" , "Sound and seem to vomit" .)