Enter with four letters from Lima after botching registration (9)
I believe the answer is:
enrolment
'registration' is the definition.
(eg enrolling at a university)
'enter with four letters' is the wordplay.
'enter' becomes 'enrol' (synonyms).
'with four letters' becomes 'ment' (I can't explain this - if you can you should believe this answer much more).
'enrol'+'ment'='ENROLMENT'
'from lima after botching' is the link.
I am not very happy about this link. Some or all of it may belong to another bit of the clue.
Can you help me to learn more?
(Other definitions for enrolment that I've seen before include "Act of entering on a list of members" , "matriculation" , "Registration" , "signing up" , "Joining" .)