Leather had influence reportedly (5)
I believe the answer is:
suede
'leather' is the definition.
(I know that suede is a leather)
'had influence reportedly' is the wordplay.
'had influence' becomes 'swayed'.
'reportedly' shows a homophone (sound like).
'swayed' sounds like 'SUEDE'.
(Other definitions for suede that I've seen before include "leather material" , "unprepared material" , "Soft goatskin" , "Soft, velvety leather" , "Kid possibly" .)