Old lady spat on Republican, giving tissue (6)
I believe the answer is:
marrow
'tissue' is the definition.
(marrow is a kind of tissue)
'old lady spat on republican' is the wordplay.
'old lady' becomes 'ma' (both can informally mean mother).
'spat' becomes 'row' (I've seen this in another clue).
'on' is a charade indicator (letters next to each other).
'republican' becomes 'R' (abbreviation in US politics).
'row' put after 'r' is 'rrow'.
'ma'+'rrow'='MARROW'
'giving' acts as a link.
(Other definitions for marrow that I've seen before include "Fatty stuff in bones, or a vegetable gourd" , "Matter in bones or a vegetable" , "Bone filler" , "Connective tissue in bones" , "The best part" .)