Register for (5)
'register for' is the definition.
(as in registering for or entering a competition)
This is the entire clue.
(Other definitions for enter that I've seen before include "Gain admission" , "put in for a race" , "Infiltrate" , "Record - stage direction - come in" , "Go/come in" .)
(Other definitions for enrol that I've seen before include "Sign on, register" , "Sign on, being a loner" , "Add to list of members" , "register for classes" , "Bring into service" .)
(Other definitions for sign up that I've seen before include "Enlist" , "Engage by written agreement" , "join the ranks" , "Commit to employment, education, etc" , "Take on" .)