Minor act possibly becoming sentimental (8)
I believe the answer is:
romantic
'sentimental' is the definition.
(I've seen this in another clue)
'minor act possibly' is the wordplay.
'possibly' is an anagram indicator.
'minor'+'act'='minoract'
'minoract' anagrammed gives 'ROMANTIC'.
'becoming' is the link.
(Other definitions for romantic that I've seen before include "Soulful or amourous idealist" , "Amorous (but not practical?)" , "Having an idealised view of reality" , "Involving a love affair, appealing to the tender emotions" , "Visionary" .)