The tenant has not as much ease, they say (6)
I believe the answer is:
lessee
'the tenant' is the definition.
(lessee is a kind of tenant)
'not as much ease they say' is the wordplay.
'not as much' becomes 'less' (similar in meaning).
'they say' indicates a 'sounds like' (homophone) clue.
'ease' sounds like 'ee'.
'less'+'ee'='LESSEE'
'has' is the link.
(Other definitions for lessee that I've seen before include "Who pays the rent" , "One who rents" , "One holds a lease" , "The one taking out lease" , "Contractor" .)