Latin fellow leaves after, more tardy (5)
I believe the answer is:
later
'more tardy' is the definition.
('late' can be a synonym of 'tardy')
'latin fellow leaves after' is the wordplay.
'latin' becomes 'l'.
'fellow' becomes 'F' (abbreviation - of a society etc.).
'leaves' is a deletion indicator.
'after' with 'f' taken away is 'ater'.
'l'+'ater'='LATER'
(Other definitions for later that I've seen before include "after the rest?" , "Afterward, subsequent" , "After a given point in time" , "Tomorrow (or next week)?" , "Eventually" .)