Abominable snowman — the old-time one? (4)
I believe the answer is:
yeti
'abominable snowman' is the definition.
(I've seen this in another clue)
'the old-time one?' is the wordplay.
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'time' becomes 't' (abbreviation).
'one?' becomes 'I' (Roman numeral).
'ye'+'t'+'i'='YETI'
(Other definitions for yeti that I've seen before include "Highly elusive monster" , "The Abominable Snowman in Tibetan" , "Creature perhaps" , "creature of dubious existence" , "seeks him in the Himalayas" .)