An exhausting thing to do, though the purpose is lofty (3,2)
I believe the answer is:
use up
'an exhausting thing to do' is the definition.
I can't judge whether this definition defines the answer.
'the purpose is lofty' is the wordplay.
'the purpose' becomes 'use' (synonyms).
'is lofty' becomes 'up' (I can't justify this - if you can you should give a lot more credence to this answer).
'use'+'up'='USE UP'
'though' acts as a link.
Can you help me to learn more?
(Other definitions for use up that I've seen before include "Exhaust (resources)" , "Entirely consume" , "Consume (stocks)" , "Finish, exhaust" , "Expend" .)