Function with princess and earl without a fixed date in Rome (4,3)
I believe the answer is:
sine die
'without a fixed date in rome' is the definition.
(Latin phrase meaning with no appointed date)
'function with princess and earl' is the wordplay.
'function' becomes 'sine' (mathematical function).
'with' says to put letters next to each other.
'princess' becomes 'di' (Princess Diana).
'and' is a charade indicator (letters next to each other).
'earl' becomes 'e'.
'sine'+'di'+'e'='SINE DIE'
(Other definitions for sine die that I've seen before include "With no date set for resumption (Latin)" , "Indefinitely (Latin, as applied to sporting suspensions)" , "Postponed indefinitely (L.)" , "For an indefinite period (Latin)" , "With no appointed date for resumption (Latin)" .)