Stick out for a planned undertaking (7)
I believe the answer is:
project
I believe this clue is a double definition.
'stick out' is the first definition.
('project' can be a synonym of 'stick out')
'a planned undertaking' is the second definition.
(I've seen this before)
'for' is the link.
(Other definitions for project that I've seen before include "low-cost housing" , "Scheme - stick out!" , "Jut out" , "Planned enterprise" , "Venture" .)