Lizard originally given every care keepers offer (5)
I believe the answer is:
gecko
'lizard' is the definition.
(gecko is a kind of lizard)
'originally given every care keepers offer' is the wordplay.
'originally' says to take the initial letters.
The initial letters of 'given every care keepers offer' is 'GECKO'.
(Other definitions for gecko that I've seen before include "House lizard" , "Lizard noted for ability to climb smooth surfaces" , "Thick-bodied lizard" , "Nocturnal lizard" , "one climbing the walls?" .)