Tenant, heading off to get key (5)
I believe the answer is:
enter
'key' is the definition.
(key on a computer keyboard)
'tenant heading off' is the wordplay.
'tenant' becomes 'renter' (someone renting a property).
'heading off' means to remove the first letter.
'renter' with its first letter taken away is 'ENTER'.
'to get' acts as a link.
(Other definitions for enter that I've seen before include "Pierce" , "Record (in a log)" , "Move into" , "cross the threshold" , "Introduce" .)