You need a verb to have a clause.
I think you meant "The GMC cannot investigate every
controversial treatment brought to its attention".
[NP every controversial treatment [CLAUSE [NP PRO (which) ] [VP (is) brought [PP to its attention]] ] ]
The clause serves an adjectival function, but the structure as a whole is a noun phrase functioning as direct object within the entire sentence.
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... use gentle persuasion to get industries to reduce waste.
[ VP use [NP gentle persuasion ]
[ CLAUSE [ NP PRO (agency)] [VP to get [ CLAUSE [NP industries ] [ VP to reduce [NP waste] endVP] endCLAUSE ] endVP] endCLAUSE] endVP]
This verb phrase has a clause within another clause. The outer clause is a causative ("get"), so it has an inner clause "industries to reduce waste" which is the direct object of the causative. The whole outer clause "to get industries ..." is an adverbial adjunct to the verb phrase which precedes it (adverbial of purpose).
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This isn't nearly as complicated as a real linguist would see it!
![Smile [:)]](/emoticons/emotion-1.gif)