Refined what some tenants may do when rent finally gets raised (6)
I believe the answer is:
subtle
'refined' is the definition.
(I've seen this before)
I can't explain the rest of the clue.
(Other definitions for subtle that I've seen before include "Not immediately obvious, understated" , "Tenuous; refined" , "Fine, delicate or elusive" , "Ingenious, difficult to analyse" , "Slight and difficult to analyse, as distinction may be" .)