Make fullest use of proverb first to explain gripping lives (8)
I believe the answer is:
maximise
'make fullest use' is the definition.
I don't know anything about this answer so I cannot judge whether this works.
'proverb first to explain gripping lives' is the wordplay.
'proverb' becomes 'maxim' (I've seen this before).
'first to' indicates taking the first letters.
'gripping' is an insertion indicator (inserted letters are gripped).
'lives' becomes 'is' ('be' can be a synonym of 'live').
The initial letter of 'explain' is 'e'.
'maxim'+'e'='maxime'
'maxime' placed around 'is' is 'MAXIMISE'.
'of' acts as a link.
Can you help me to learn more?
(Other definitions for maximise that I've seen before include "Make the best use of" , "Make as big as possible" , "Make as large as possible" .)