One is free to contact institute that has, well ? a hard element (7)
I believe the answer is:
iridium
'element' is the definition.
(iridium is a kind of element)
'one is free to contact institute that has' is the wordplay.
'one' becomes 'I' (Roman numeral).
'is free' becomes 'rid' (to be free of something is to be rid of it).
'to contact' becomes 'um' (I am not sure about this - if you are sure you should believe this answer much more).
'institute' becomes 'i' (common abbreviation as in MIT).
'that has' is a charade indicator (letters next to each other).
'um' after 'i' is 'ium'.
'i'+'rid'+'ium'='IRIDIUM'
'well ? a hard' acts as a link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for iridium that I've seen before include "Heavy brittle metal used in alloys, Ir" , "Element, symbol Ir" , "Hard metallic element" , "Hard silvery metal" , "Corrosion-resistant metal, Ir" .)