Liveliness of brother crossing island (4)
I believe the answer is:
brio
'liveliness' is the definition.
(thesaurus)
'brother crossing island' is the wordplay.
'brother' becomes 'bro' (**).
'crossing' indicates putting letters inside.
'island' becomes 'i'.
'bro' enclosing 'i' is 'BRIO'.
'of' acts as a link.
(Other definitions for brio that I've seen before include "Vigour, vivacity" , "Enthusiasm" , "Drive" , "Animation (Italian)" , "Spiritedness" .)