Follow guarantee ignoring Republican (5)
I believe the answer is:
ensue
'follow' is the definition.
(ensue can mean to follow or happen as a result)
'guarantee ignoring republican' is the wordplay.
'guarantee' becomes 'ensure' (synonyms).
'ignoring' suggests deleting specific letters.
'republican' becomes 'R' (abbreviation in US politics).
'ensure' with 'r' removed is 'ENSUE'.
(Other definitions for ensue that I've seen before include "Result in a particular way" , "Occur as a result (of)" , "Come to pass" , "Befall" , "Follow as a consequence" .)