Following end of chase, evil US criminal is hard to find (7)
I believe the answer is:
elusive
'hard to find' is the definition.
(I've seen this before)
'following end of chase evil us criminal' is the wordplay.
'following' means one lot of letters go next to another.
'end of' indicates one should take the final letters.
'criminal' indicates anagramming the letters.
The final letter of 'chase' is 'e'.
'evil'+'us'='evilus'
'evilus' is an anagram of 'lusive'.
'e' next to 'lusive' is 'ELUSIVE'.
'is' acts as a link.
(Other definitions for elusive that I've seen before include "Use veil to be difficult to catch" , "Not easy to pin down" , "Hard to grasp" , "Difficult to grasp" , "Evasive or intangible" .)