Stubborn American soldier in Republican papers (5)
I believe the answer is:
'stubborn' is the definition.
'american soldier in republican papers' is the wordplay.
'american soldier' becomes 'GI' (informal term for a US soldier).
'in' indicates putting letters inside.
'republican' becomes 'R' (abbreviation).
'papers' becomes 'id' (short for identification papers).
'gi' inserted within 'rid' is 'RIGID'.
(Other definitions for rigid that I've seen before include "Stiff and inflexible" , "stern" , "not relaxing" , "Frozen" , "Incapable of or resistant to bending" .)