In life, king's vigour (4)
I believe the answer is:
brio
'vigour' is the definition.
(I've seen this before)
'in life king's' is the wordplay.
'in' means one lot of letters goes inside another.
'life' becomes 'bio' (life can mean a biography).
'king' becomes 'R' (abbreviation of Latin rex).
'bio' placed around 'r' is 'BRIO'.
(Other definitions for brio that I've seen before include "(Of music) spirit" , "Vivacity - spirit" , "Drive" , "Vivacity of style" , "In music, con ..... means with dash and verve" .)