Legal right to possess chestnut fungus and alga (6)
I believe the answer is:
lichen
'fungus and alga' is the definition.
(composite organism of both)
'legal right to possess chestnut' is the wordplay.
'legal right' becomes 'lien' (I've seen this before).
'to possess' means one lot of letters goes inside another.
'chestnut' becomes 'ch' (I've seen this in other clues).
'lien' going around 'ch' is 'LICHEN'.
(Other definitions for lichen that I've seen before include "Growth found on tree trunks and rocks" , "Crusty, tufty growth on trees and stones" , "Tiny green-grey plants growing on rocks and trees" , "Compound plant not unlike to moss in appearance" , "Compound plant of fungus and alga" .)