Follow, hugging right path (5)
I believe the answer is:
trail
'path' is the definition.
(I know that trail is a type of path)
'follow hugging right' is the wordplay.
'follow' becomes 'tail' (both can mean to chase or pursue).
'hugging' indicates putting letters inside.
'right' becomes 'r' (common abbreviation).
'tail' going around 'r' is 'TRAIL'.
(Other definitions for trail that I've seen before include "Drag behind" , "Spoor - lag behind" , "Drop behind" , "Beaten path; lag" , "Rough track blazed through wild or hilly country" .)