Search all over the place for horse (6)
I believe the answer is:
chaser
'for horse' is the definition.
(type of horse)
'search all over the place' is the wordplay.
'all over the place' indicates anagramming the letters.
'search' is an anagram of 'CHASER'.
(Other definitions for chaser that I've seen before include "Beer after whisky, say (or vice versa)" , "Hunter; drink" , "different drink to follow" , "A drink like beer after whisky" , "Beer after whisky - follow that!" .)