Developed at last the battery's storage capacity (8)
I believe the answer is:
terabyte
'storage capacity' is the definition.
'developed at last the battery's' is the wordplay.
'developed' indicates anagramming the letters.
'at last' suggests the final letters.
The last letter of 'the' is 'e'.
'e'+'battery'='ebattery'
'ebattery' is an anagram of 'TERABYTE'.
(Other definitions for terabyte that I've seen before include "Large unit of computer memory" , "1000 gigabytes of data information" .)