Muntjac, possibly, bringing up grass (4)
I believe the answer is:
deer
'muntjac possibly' is the definition.
(muntjac is a kind of deer)
'up grass' is the wordplay.
'up' says the letters should be written in reverse (in down clue: letters go upwards).
'grass' becomes 'reed' (type of grass plant).
'reed' in reverse letter order is 'DEER'.
'bringing' acts as a link.
(Other definitions for deer that I've seen before include "Perhaps fallow" , "maybe does" , "Ruminant(s) -- breed of 13 down" , "Sledge animals for Father Christmas" , "Eg, stag or doe" .)