Greens regularly pressing to be on the rise again (9)
I believe the answer is:
resurgent
'be on the rise again' is the definition.
'greens regularly pressing' is the wordplay.
'regularly' means one should take alternating letters (regularly take one letter, leave next etc.).
'pressing' becomes 'urgent' (synonyms).
The alternate letters of 'greens' are 'res'.
'res'+'urgent'='RESURGENT'
'to' is the link.
(Other definitions for resurgent that I've seen before include "Reviving after a lull" , "Coming back to life" , "making comeback" , "rising again" , "given new life" .)