Declare in favour of application (8)
I believe the answer is:
proclaim
'declare' is the definition.
(proclaiming is a kind of declaring)
'in favour of application' is the wordplay.
'in favour of' becomes 'pro' (being pro a particular cause).
'application' becomes 'claim'.
'pro'+'claim'='PROCLAIM'
(Other definitions for proclaim that I've seen before include "Broadcast" , "Herald" , "shout from the housetops" , "Reveal" , "Speak out" .)