Run to leave tenant key (5)
I believe the answer is:
enter
'key' is the definition.
(key on a computer keyboard)
'run to leave tenant' is the wordplay.
'run' becomes 'r' (cricket abbreviation).
'to leave' suggests deleting specific letters.
'tenant' becomes 'renter' ('renter' can be a synonym of 'tenant').
'renter' with 'r' removed is 'ENTER'.
(Other definitions for enter that I've seen before include "Come or go in" , "Introduce" , "Get in" , "Treen (anag.)" , "Move into" .)