Old and dull doctor that is descending on Irish party (5-2)
I believe the answer is:
dried-up
'old and dull' is the definition.
(dried-up can mean old and boring)
'doctor that is descending on irish party' is the wordplay.
'doctor' becomes 'dr' (abbreviation).
'that is' becomes 'ie' (abbreviation for id est, 'that is' in Latin).
'descending on' is a charade indicator (letters next to each other) (in a down clue, some letters go on top of others).
'irish party' becomes 'dup' (Democratic Unionist Party).
'dr'+'ie'+'dup'='DRIED-UP'
(Another definition for dried-up that I've seen is " Failed - wiped dishes - forgot lines".)