Tick found around very big desert is bloodsucker (8)
I believe the answer is:
mosquito
'is bloodsucker' is the definition.
(thesaurus)
'tick found around very big desert' is the wordplay.
'tick' becomes 'mo' (both can mean a very short amount of time).
'found around' means one lot of letters goes inside another.
'very big' becomes 'os' (abbreviation for outsize).
'desert' becomes 'quit' (I've seen this before).
'os'+'quit'='osquit'
'mo' enclosing 'osquit' is 'MOSQUITO'.
(Other definitions for mosquito that I've seen before include "Disease-carrying insect" , "droning irritant" , "Malaria-carrying insect" , "Flying biting insect" , "Disease-spreading insect" .)