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 mean mother).
'spat' becomes 'row' (I've seen this in another clue).
'on' means one lot of letters go next to another.
'republican' becomes 'R' (abbreviation in US politics).
'row' after 'r' is 'rrow'.
'ma'+'rrow'='MARROW'
'giving' is the 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" .)