Now and then turn out for brisk walk (4)
I believe the answer is:
trot
'brisk walk' is the definition.
'now and then turn out' is the wordplay.
'now and then' means one should take alternating letters (letters taken on a regular basis, now and then).
'turn'+'out'='turnout'
The alternating letters of 'turnout' are 'TROT'.
'for' acts as a link.
(Other definitions for trot that I've seen before include "Horse's gait - extreme leftist" , "movement of H [TROT]" , "Hurry along" , "Go at steady pace" , "Follower of revolutionary" .)