Authorise small step around moon finally (8)
I believe the answer is:
sanction
'authorise' is the definition.
(sanctioning is a kind of authorising)
'small step around moon finally' is the wordplay.
'small' becomes 's' (abbreviation - e.g. clothes size).
'step' becomes 'action' (**).
'around' indicates putting letters inside.
'finally' suggests the final letters.
The final letter of 'moon' is 'n'.
'action' going around 'n' is 'anction'.
's'+'anction'='SANCTION'
(Other definitions for sanction that I've seen before include "Penalty for breaking law" , "Agree to - penalty" , "Give official approval or attach a penalty to" , "Support" , "Authorisation" .)