Elevator gets trainee terribly fit (4)
I believe the answer is:
lift
'elevator' is the definition.
('lift' can be a synonym of 'elevator')
'trainee terribly fit' is the wordplay.
'trainee' becomes 'l'.
'terribly' indicates an anagram.
'fit' with letters rearranged gives 'ift'.
'l'+'ift'='LIFT'
'gets' is the link.
(Other definitions for lift that I've seen before include "remove" , "Steal (colloq.); elevator" , "Pick up" , "Exalt" , "Raise - hoist" .)