Chase down weak animal round with heart aflutter (3,2,5)
I believe the answer is:
run to earth
'chase down' is the definition.
(to run someone to earth is to track them down)
'weak animal round with heart aflutter' is the wordplay.
'weak animal' becomes 'runt' (as in the runt of the litter).
'round' becomes 'o' (round can mean a round object).
'with' means one lot of letters go next to another.
'aflutter' indicates an anagram (I've seen this in other clues).
'heart' is an anagram of 'earth'.
'runt'+'o'+'earth'='RUN TO EARTH'
(Other definitions for run to earth that I've seen before include "Find after searching" , "Discover" , "Track down" , "Search out, find" , "what one must do with ground lead" .)