Conservative from America's heart to submit (5)
I believe the answer is:
enter
'to submit' is the definition.
(as in to submit something to a competition)
I cannot understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for enter that I've seen before include "Go in and put in the ledger" , "Introduce" , "Record - stage direction - come in" , "Come or go in" , "Register formally as a participant" .)