Writer of biography introducing Republican (4)
I believe the answer is:
biro
'writer' is the definition.
(type of pen, something which writes)
'of biography introducing republican' is the wordplay.
'of biography' becomes 'bio' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'introducing' means one lot of letters goes inside another (some letters introduced or inserted into others).
'republican' becomes 'R' (abbreviation in US politics).
'bio' going around 'r' is 'BIRO'.
Can you help me to learn more?
(Other definitions for biro that I've seen before include "Writing implement" , "writer" , "Pocket item" , "Lazlo -, ballpoint pen inventor" , "Laszlo Jozsef -, ballpoint pen inventor" .)