Study and given a test, I fancy (11)
I believe the answer is:
investigate
'study' is the definition.
(investigating is a kind of studying)
'given a test i fancy' is the wordplay.
'fancy' indicates an anagram.
'given'+'a'+'test'+'i'='givenatesti'
'givenatesti' is an anagram of 'INVESTIGATE'.
'and' acts as a link.
(Other definitions for investigate that I've seen before include "carry out a formal enquiry" , "Search" , "Enquire into" , "check out" , "Examine" .)