Dramatist has irrational residue running around (9)
I believe the answer is:
euripides
'dramatist' is the definition.
(I know that Euripides is a dramatist)
'irrational residue running around' is the wordplay.
'irrational' becomes 'pi' (an irrational number).
'running' indicates anagramming the letters.
'around' indicates putting letters inside.
'residue' anagrammed gives 'eurides'.
'pi' going into 'eurides' is 'EURIPIDES'.
'has' acts as a link.
(Other definitions for euripides that I've seen before include "playmaker" , "Classical playwright (Alcestis, Electra, etc)" , "Ancient Greek dramatist" , "Athenian playwright" , "old dramatist" .)