The old part-time Himalayan Bigfoot (4)
I believe the answer is:
yeti
'the old part-time himalayan bigfoot' is the definition.
'yeti' can be an answer for 'bigfoot' (I've seen this before). I'm not sure about the 'the old part-time himalayan' bit.
'the old part' is the wordplay.
'the old' becomes 'ye' (resembles a historical spelling of 'the').
'part' becomes 'ti' (ti is a kind of part).
'ye'+'ti'='YETI'
Can you help me to learn more?
(Other definitions for yeti that I've seen before include "Creature of disputed existence" , "Tibetan creature" , "imaginary beast?" , "hirsute specimen" , "Hairy creature of legend" .)