Bird finally caught rodent eating it (8)
I believe the answer is:
titmouse
'bird' is the definition.
(titmouse is a kind of bird)
'finally caught rodent eating it' is the wordplay.
'finally' suggests the final letters.
'rodent' becomes 'mouse' (mouse is a kind of rodent**).
'eating' means one lot of letters goes inside another.
The last letter of 'caught' is 't'.
't'+'mouse'='tmouse'
'tmouse' placed around 'it' is 'TITMOUSE'.
(Other definitions for titmouse that I've seen before include "Small bird" , "Small songbird" .)