The alien constituents saw has them on edge (5)
I believe the answer is:
teeth
'edge' is the definition.
(thesaurus)
'the alien constituents saw has them' is the wordplay.
I cannot quite see how this works, but
an anagram of 'the' is 'eth' which is located in the answer.
The remaining letters 'te' is a valid word which might be clued in a way I don't understand.
This may be the basis of the clue (or it may be nonsense).
'on' is the link.
Can you help me to learn more?
(Other definitions for teeth that I've seen before include "Canines, molars, etc" , "Structures in the jaw" , "Choppers" , "Genuine effectiveness" , "Power to enforce" .)