Very keen to have a look into god (7)
I believe the answer is:
zealous
'very keen' is the definition.
(I've seen this before)
'a look into god' is the wordplay.
'look' becomes 'lo' (archaic term meaning 'look!').
'into' indicates putting letters inside.
'god' becomes 'zeus' (Zeus is an example).
'a'+'lo'='alo'
'alo' put into 'zeus' is 'ZEALOUS'.
'to have' acts as a link.
(Other definitions for zealous that I've seen before include "Fanatical" , "Avidly enthusiastic" , "Ardently active" , "Avid" , "Fervent" .)