Regularly upbeat, much-liked (3)
I believe the answer is:
pet
'much-liked' is the definition.
(as in a pet project)
'regularly upbeat' is the wordplay.
'regularly' indicates alternate letters (regularly take one letter, leave next etc.).
The alternating letters of 'upbeat' are 'PET'.
(Other definitions for pet that I've seen before include "Tame animal kept for companionship" , "Tamed domestic animal" , "Favourite, may be teacher's" , "Preferred" , "Favourite - maybe teacher's" .)