Closely follow tailless mammoth (3)
I believe the answer is:
hug
'closely follow' is the definition.
(as in to keep close to something when moving)
'tailless mammoth' is the wordplay.
'tailless' means to remove the last letter.
'mammoth' becomes 'huge' (synonyms).
'huge' with its last letter taken away is 'HUG'.
(Other definitions for hug that I've seen before include "Tight embrace" , "Cuddle" , "Embrace (like a bear?)" , "Tightly embrace" , "Clasp" .)