Girl outside seedy Irish club (10)
I believe the answer is:
shillelagh
'irish club' is the definition.
(Irish club used as a weapon)
'girl outside seedy' is the wordplay.
'girl' becomes 'shelagh' (girl's name).
'outside' is an insertion indicator.
'seedy' becomes 'ill' (seedy can mean unwell).
'shelagh' placed around 'ill' is 'SHILLELAGH'.
(Other definitions for shillelagh that I've seen before include "Irish club" , "Irish cudgel" .)