Being a primate is in fashion, old man reflected (6)
I believe the answer is:
apedom
'being a primate' is the definition.
(state of being an ape)
'fashion old man reflected' is the wordplay.
'fashion' becomes 'mode' (synonyms).
'old man' becomes 'pa' (both can mean father).
'reflected' says the letters should be written in reverse.
'mode'+'pa'='modepa'
'modepa' reversed gives 'APEDOM'.
'is in' acts as a link.
(Other definitions for apedom that I've seen before include "Where primates are found" , "class of swingers?" , "condition of primates" .)