Register ultimate in danger is involved in solo climbing (5)
'register' is the definition.
(enrolling is a kind of registering)
'ultimate in danger is involved in solo climbing' is the wordplay.
'ultimate in' indicates one should take the final letters.
'is involved in' means one lot of letters goes inside another.
'solo' becomes 'lone' (both can mean alone).
'climbing' says the letters should be written backwards (in a down clue, letters climb up).
The last letter of 'danger' is 'r'.
'r' going into 'lone' is 'lorne'.
'lorne' reversed gives 'ENROL'.
(Other definitions for enrol that I've seen before include "Register officially", "Register (as student)", "Insert in register", "Enlist", "Join up, sign on".)