The desire to get out of Mitchum (4)
I believe the answer is:
itch
'the desire' is the definition.
(itch is a kind of desire)
'out of mitchum' is the wordplay.
'out of' indicates the answer is hidden within the clue.
'ITCH' is hidden in the letters of 'mitchum'.
'to get' is the link.
(Other definitions for itch that I've seen before include "Something that needs a scratch" , "Slight irritation" , "great desire" , "Impatient desire (colloq.)" , "Skin sensation; desire" .)