Use a lot of energy, a shade overeagerly at first (3,4)
I believe the answer is:
eat into
'use a lot of' is the definition.
'energy a shade overeagerly at first' is the wordplay.
'energy' becomes 'e' (physics symbol as in E=mci).
'shade' becomes 'tint' (synonyms).
'at first' suggests taking the first letters.
The first letter of 'overeagerly' is 'o'.
'e'+'a'+'tint'+'o'='EAT INTO'
(Other definitions for eat into that I've seen before include "Etch" , "start wearing out" , "Corrode (something)" , "Consume (resources)" , "run down" .)