Use up a bit of energy doing no good around north Ohio (3,4)
I believe the answer is:
eat into
'use up' is the definition.
(synonyms)
'a bit of energy doing no good around north ohio' is the wordplay.
'bit of' suggests taking the first letters.
'doing' indicates anagramming the letters (doing can mean solving or working out).
'no good around north ohio' becomes 'tinto' (I can't justify this - if you can you should give a lot more credence to this answer).
The initial letter of 'energy' is 'e'.
'a'+'e'='ae'
'ae' is an anagram of 'ea'.
'ea'+'tinto'='EAT INTO'
Can you help me to learn more?
(Other definitions for eat into that I've seen before include "Etch" , "Consume (resources)" , "run down" , "start wearing out" , "Corrode (something)" .)