Small show of joy perhaps, after rent reduction (8)
I believe the answer is:
teardrop
'small show of joy perhaps' is the definition.
(as in tears of joy)
'after rent reduction' is the wordplay.
'after' means one lot of letters go next to another.
'rent' becomes 'tear' (synonyms).
'reduction' becomes 'drop'.
'tear' next to 'drop' is 'TEARDROP'.
(Other definitions for teardrop that I've seen before include "Visible result of crying" , "Little sign of regret" , "Parroted (anag.)" , "It falls from the eye" , "Bit of salty moisture" .)