Ticks abandon old fly (8)
I believe the answer is:
mosquito
'fly' is the definition.
(I've seen this before)
'ticks abandon old' is the wordplay.
'ticks' becomes 'mos' (a mo is a very short period of time).
'abandon' becomes 'quit' (quitting is a kind of abandoning).
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'mos'+'quit'+'o'='MOSQUITO'
(Other definitions for mosquito that I've seen before include "possible disease carrier" , "Disease-bearing fly" , "Disease-spreading insect" , "British WWII multi-role combat aircraft" , "Annoying insect" .)