The old lady mugs up on remarkable person's greatest work (6,4)
I believe the answer is:
magnum opus
'person's greatest work' is the definition.
(someone's magnum opus is their greatest work)
'the old lady mugs up on remarkable' is the wordplay.
'the old lady' becomes 'ma' (both can mean mother).
'remarkable' is an anagram indicator.
'mugs'+'up'+'on'='mugsupon'
'mugsupon' is an anagram of 'gnumopus'.
'ma'+'gnumopus'='MAGNUM OPUS'
(Other definitions for magnum opus that I've seen before include "one's best" , "great achievement" , "Creative feat" , "Writer's greatest work" , "Greatest work of an artist" .)